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Algebraic integer which represents an ideal in a ring of integers
In number theory, an ideal number is an algebraic integer which represents an ideal in the ring of integers of a number field; the idea was developed by
Ideal_number
Submodule of a mathematical ring
even number by any integer (even or odd) results in an even number; these closure and absorption properties are the defining properties of an ideal. An
Ideal_(ring_theory)
In number theory, measure of non-unique factorization
In mathematics, the ideal class group (or class group) of an algebraic number field K {\displaystyle K} is the quotient group J K / P K {\displaystyle
Ideal_class_group
Branch of number theory
factorization, the behavior of ideals, and the Galois groups of fields, can resolve questions of primary importance in number theory, like the existence of
Algebraic_number_theory
Ideal in a ring which has properties similar to prime elements
algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers. The prime ideals for the integers
Prime_ideal
algebra, the norm of an ideal is a generalization of a norm of an element in the field extension. It is particularly important in number theory since it measures
Ideal_norm
Numbers with many divisors
highly composite numbers as he deliberately chose such a number, 5040 (= 7!), as the ideal number of citizens in a city. Furthermore, Vardoulakis and Pugh's
Highly_composite_number
In algebraic number theory, the different ideal (sometimes simply the different) is defined to measure the (possible) lack of duality in the ring of integers
Different_ideal
Difference between successive eigenvalues
division in the underlying data structure, helping to determine the ideal number of clusters. Eigenvalue perturbation Spectral gap Davis, C.; W. M. Kahan
Eigengap
more specifically ring theory, an ideal I of a ring R is said to be a nilpotent ideal if there exists a natural number k such that I k = 0. By I k, it is
Nilpotent_ideal
Submodule of fractions in abstract algebra
fractional ideals of an integral domain are like ideals where denominators are allowed. In contexts where fractional ideals and ordinary ring ideals are both
Fractional_ideal
Equation of the state of a hypothetical ideal gas
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior
Ideal_gas_law
Dutch e-commerce payment system
iDEAL is an e-commerce payment system used for online banking in the Netherlands. Previously controlled by the Dutch e-commerce organization Currence
IDEAL
Concept in commutative algebra
primary ideal if p {\displaystyle p} is a prime number. The notion of primary ideals is important in commutative ring theory because every ideal of a Noetherian
Primary_ideal
Mathematical model which approximates the behavior of real gases
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept
Ideal_gas
Natural number
convenient number to use for dividing many things (including both the citizens and the land of a city-state or polis) into lesser parts, making it an ideal number
5040_(number)
Mathematical object
mathematics, ideal lattices are a special class of lattices and a generalization of cyclic lattices. Ideal lattices naturally occur in many parts of number theory
Ideal_lattice
specifically ring theory, a left, right or two-sided ideal of a ring is said to be a nil ideal if all of its elements are nilpotent, i.e. for each a
Nil_ideal
Indian profession
India. In July 2013, the number of ASHAs in India was reported to be 870,089. In 2018, this number rose to 939,978. The ideal number of ASHAs envisaged was
Accredited Social Health Activist
Accredited_Social_Health_Activist
Style of amateur wrestling
certain number. If an ideal number is not reached to begin elimination rounds, a qualification round will take place to eliminate the excess number of wrestlers
Greco-Roman_wrestling
Spanish card game
principal objective of the game is to get four cards of the same number. The ideal number of players is from 4 to 8. The objective of the game is to run
Burro_(card_game)
Every nonzero proper ideal in the ring of integers of a number field factorizes uniquely
In number theory, the fundamental theorem of ideal theory in number fields states that every nonzero proper ideal in the ring of integers of a number field
Fundamental theorem of ideal theory in number fields
Fundamental_theorem_of_ideal_theory_in_number_fields
Field extension of the rational numbers by a primitive root of unity
rings of integers—that Ernst Kummer first introduced the concept of an ideal number and proved his celebrated congruences. For n ≥ 1 {\displaystyle n\geq
Cyclotomic_field
Concept in algebra
Taking the radical of an ideal is called radicalization. A radical ideal (or semiprime ideal or reduced ideal) is an ideal that is equal to its radical
Radical_of_an_ideal
Ideal of a ring contained in no other ideal except the ring itself
maximal ideal is a two-sided ideal that is maximal (with respect to set inclusion) amongst all proper ideals. In other words, I is a maximal ideal of a ring
Maximal_ideal
Theorem in class field theory on mappings induced by extending ideals
mathematics, the principal ideal theorem of class field theory, a branch of algebraic number theory, says that extending ideals gives a mapping on the class
Principal_ideal_theorem
Indian motorcycle company (1960–1996)
Ideal Jawa (India) Ltd was an Indian motorcycle company based in Mysore, which sold licensed Jawa motorcycles beginning in 1960 under the brand name Jawa
Ideal_Jawa
1987 studio album by Wire
and released the Snakedrill EP in 1986 after reuniting). The Ideal Copy peaked at number 87 in the UK albums chart. Wire had used electronic instruments
The_Ideal_Copy
Descendants of Jacob in the Abrahamic religions
as part of the Israelite national founding myth: the number 12 was an ideal number, which had symbolic significance in Near Eastern cultures with duodecimal
Twelve_Tribes_of_Israel
Rule in math and political science
methods. It says that the number of seats allocated to a party should be equal to their entitlement plus or minus one. The ideal number of seats for a party
Quota_rule
Provides an asymptotic formula for counting the number of prime ideals of a number field
In algebraic number theory, the prime ideal theorem is the number field generalization of the prime number theorem. It provides an asymptotic formula
Landau_prime_ideal_theorem
the Fitting ideals of a finitely generated module over a commutative ring describe the obstructions to generating the module by a given number of elements
Fitting_ideal
Concept in document classification
the online store, and reduce future shopping intentions. In LIS, the ideal number of terms that should be assigned to classify an item are measured by
Overcategorization
Integers have unique prime factorizations
ideal domains. In 1843 Kummer introduced the concept of ideal number, which was developed further by Dedekind (1876) into the modern theory of ideals
Fundamental theorem of arithmetic
Fundamental_theorem_of_arithmetic
Limits ideals to be checked in order to determine the class number of a number field
algebraic number theory, Minkowski's bound gives an upper bound of the norm of ideals to be checked in order to determine the class number of a number field
Minkowski's_bound
Measurement of sleep duration
Sampasa-Kanyinga, Hugues (2018-11-27). "Sleeping hours: what is the ideal number and how does age impact this?". Nature and Science of Sleep. 10: 421–430
Sleep_efficiency
commutative algebra, the multiplier ideal associated to a sheaf of ideals over a complex variety and a real number c consists (locally) of the functions
Multiplier_ideal
Shape in hyperbolic geometry
test whether a polyhedron has an ideal version, in polynomial time. Every two ideal polyhedra with the same number of vertices have the same surface
Ideal_polyhedron
Relationship between volume and amount of a gas at constant temperature and pressure
case of the ideal gas law. A modern statement is: "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules
Avogadro's_law
Theory of ideals in commutative rings in mathematics
In mathematics, ideal theory is the theory of ideals in commutative rings. While the notion of an ideal exists also for non-commutative rings, a much
Ideal_theory
Aspect of algebraic number theory
Galois extension L of a number field K, and the way the prime ideals P of the ring of integers OK factorise as products of prime ideals of OL, provides one
Splitting of prime ideals in Galois extensions
Splitting_of_prime_ideals_in_Galois_extensions
Physical constant equivalent to the Boltzmann constant, but in different units
gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol R or R. It is the molar equivalent
Gas_constant
Non-empty family of sets that is closed under finite unions and subsets
mathematics, an ideal on a set is a family of subsets that is closed under subsets and finite unions. Informally, sets that belong to the ideal are considered
Ideal_on_a_set
Statistics and machine learning technique
for determining the proper number of components. More recently, a theoretical framework suggested that there is an ideal number of component classifiers
Ensemble_learning
1979 video game
game created by Ralph H. Baer (the inventor of Simon), and released by the Ideal Toy Company. Maniac is "four games in one". Instructions refer to the individual
Ideal_Maniac
Used to count, measure, and label
A number is a mathematical object used to count, measure, order and label. The most basic examples are the natural numbers: 1, 2, 3, 4, 5, and so forth
Number
Number divisible only by 1 and itself
numbers include prime elements and prime ideals. A natural number (1, 2, 3, 4, 5, 6, etc.) is called a prime number (or a prime) if it is greater than 1 and
Prime_number
Generalizations of prime ideals and prime rings
mathematics, semiprime ideals and semiprime rings are generalizations of prime ideals and prime rings. In commutative algebra, semiprime ideals are also called
Semiprime_ring
Type of chemical reactor
an ideal CSTR and PFR. A continuous fluid flow containing non-conservative chemical reactant A enters an ideal CSTR of volume V. perfect or ideal mixing
Continuous stirred-tank reactor
Continuous_stirred-tank_reactor
West Germanic language
[t͡ʃail] and "wind" [win]. Indian English historically tends towards RP as an ideal, with the proximity of speakers to RP generally reflecting class distinctions
English_language
field norm map and m K {\displaystyle {\mathfrak {m}}_{K}} is the maximal ideal of K {\displaystyle K} . Equivalently, n {\displaystyle n} is the smallest
Conductor (class field theory)
Conductor_(class_field_theory)
Tool used to make legislatures more proportional
Once a final ideal distribution has been settled, the number of leveling seats awarded to each party is equal to that party's ideal number of seats minus
Leveling_seat
algebraic number theory, a modulus (plural moduli) (or cycle, or extended ideal) is a formal product of places of a global field (i.e. an algebraic number field
Modulus (algebraic number theory)
Modulus_(algebraic_number_theory)
Branch of pure mathematics
abstract algebra and early ideal theory and valuation theory; see below. A conventional starting point for analytic number theory is Dirichlet's theorem
Number_theory
State of matter
number of particles. His theory was not generally accepted until 1858 when another Italian chemist Stanislao Cannizzaro was able to explain non-ideal
Gas
mathematics, especially ring theory, a regular ideal can refer to multiple concepts. In operator theory, a right ideal i {\displaystyle {\mathfrak {i}}} in a
Regular_ideal
American manufacturer of electrical connectors and tools
Ideal Industries is an American company that produces connectors, hand tools, testers, and meters for the electrical and telecommunications industries
Ideal_Industries
Sexual behavior
promiscuity study". UPI. "What's Your Number?". Onlinedoctor.superdrug.com. "The verdict is in: This is the ideal number of sexual partners to have in your
Promiscuity
Ring ideal generated by a single element of the ring
In mathematics, specifically ring theory, a principal ideal is an ideal I {\displaystyle I} in a ring R {\displaystyle R} that is generated by a single
Principal_ideal
Minimal element in the set of prime ideals ordered by inclusion
use minimal prime ideals. A prime ideal P is said to be a minimal prime ideal over an ideal I if it is minimal among all prime ideals containing I. (Note:
Minimal_prime_ideal
2020 studio album by All Them Witches
Nothing as the Ideal is the sixth studio album by American psychedelic rock band All Them Witches. It was released on September 4, 2020, through New West
Nothing_as_the_Ideal
German mathematician (1810–1893)
variety Kummer–Vandiver conjecture Kummer's transformation of series Ideal number Regular prime Reflection theorem Principalization McElroy, Tucker (2005)
Ernst_Kummer
Type of set in abstract algebra
algebraic number theory, the ideal quotient is useful while studying fractional ideals. This is because the inverse of any invertible fractional ideal I {\displaystyle
Ideal_quotient
Subspecialty of industrial engineering
need of servicing variables. Line balancing equations determine the ideal number of workers needed on a production line to enable it to work at capacity
Methods_engineering
2003 single by Biffy Clyro
UK Singles Chart, it peaked at number 46. Songs and lyrics by Simon Neil. Music by Biffy Clyro. CD (BBQ365CD) "The Ideal Height" – 3:41 "...And with the
The_Ideal_Height
First container ship
SS Ideal X, a converted World War II T-2 oil tanker, was the first commercially successful container ship. Built by The Marinship Corporation during World
SS_Ideal_X
In mathematics, the Jacobian ideal or gradient ideal is the ideal generated by the Jacobian of a function or function germ. Let O ( x 1 , … , x n ) {\displaystyle
Jacobian_ideal
Finite extension of the rationals
example is that the ring of algebraic integers of a number field is not necessarily a principal ideal domain, and not necessarily even a unique factorization
Algebraic_number_field
Digital circuit implementation method
the ideal number of full-adder elements per block is equal to the square root of the number of bits being added, since that will yield an equal number of
Carry-select_adder
Branch of algebra that studies commutative rings
Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both
Commutative_algebra
Number used for counting
\rangle } . If X {\displaystyle X} is any set and I {\displaystyle I} is an ideal of A {\displaystyle A} , then a function s I {\displaystyle s_{I}} defined
Natural_number
Theorem in commutative algebra
algebra, Krull's principal ideal theorem, named after Wolfgang Krull (1899–1971), gives a bound on the height of a principal ideal in a commutative Noetherian
Krull's principal ideal theorem
Krull's_principal_ideal_theorem
Genus of monkey
cessation of ovulation to care for the offspring of others in the group. The ideal number of caregivers for an infant marmoset has been shown to be around five
Pygmy_marmoset
Proposed amendment to the US Constitution
more than one Representative for every fifty thousand persons. The "ideal" number of seats in the House of Representatives has been a contentious issue
Congressional Apportionment Amendment
Congressional_Apportionment_Amendment
Topics referred to by the same term
(number theory), the size of the ideal class group of a number ring Class number (binary quadratic forms), the number of equivalence classes of binary
Class_number
Reduction of a ring by one of its ideals
is a maximal ideal, while R / I {\displaystyle R/I} is an integral domain if and only if I {\displaystyle I} is a prime ideal. A number of similar statements
Quotient_ring
1999 single by Ideal
R&B quartet Ideal, released on July 13, 1999 through Virgin Records as the lead single from the group's eponymous debut studio album Ideal. It was written
Get_Gone
Molecular model for describing polymers
An ideal chain (or freely-jointed chain) is the simplest model in polymer chemistry to describe polymers, such as nucleic acids and proteins. It assumes
Ideal_chain
Number of particle in a given volume of an ideal gas
constant or Loschmidt's number (symbol: n0) is the number of particles (atoms or molecules) of an ideal gas per volume (the number density), and usually
Loschmidt_constant
Measure of the force amplification achieved by using a tool
way are called mechanisms. An ideal mechanism transmits power without adding to or subtracting from it. This means the ideal machine does not include a power
Mechanical_advantage
Field (mathematics) generated by the square root of an integer
the discriminant of a quadratic field). Any prime number p {\displaystyle p} gives rise to an ideal p O K {\displaystyle p{\mathcal {O}}_{K}} in the ring
Quadratic_field
Geneticist
Hopkins University's Institute of Genetic Medicine worked to determine the ideal number of cells to use in human in utero transplantation by utilizing a human-mouse
Karin_J._Blakemore
Decision-making concept
the number of choices, the greater the likelihood that the choice set will include the optimal choice for any given consumer. As a result, the ideal number
Choice_architecture
Algebraic structure
degrees of the elements of the ideal. There are two main cases where minimal polynomials are considered. In field theory and number theory, an element θ of an
Polynomial_ring
Instruction slot being executed without the effects of a preceding instruction
prohibited or deprecated. The ideal number of branch delay slots in a particular pipeline implementation is dictated by the number of pipeline stages, the presence
Delay_slot
1978 album by Sad Café
Misplaced Ideals is the second studio album by English rock band Sad Café, released in April 1978 by RCA Records. Despite no singles being released from
Misplaced_Ideals
IDEAL (Idea, Development, Exploration, Assessment, Long-term study) is a framework for describing the stages of innovation in surgery and other interventional
IDEAL_framework
Traditional children's game from Indonesia
usually played by children around eight years of age and above. The ideal number of players is between three and ten people and it is normally played
Sepak_Tekong
When an idea extends to a principal ideal in an extension of algebraic number fields
In algebraic number theory, the concept of principalization (also called capitulation) refers to the phenomenon where an ideal (or more generally a fractional
Principalization_(algebra)
Theorem in algebraic number theory
In algebraic number theory, the Dedekind–Kummer theorem describes how a prime ideal in a Dedekind domain factors over the domain's integral closure. It
Dedekind–Kummer_theorem
Algebraic structure with addition and multiplication
of integers of a number field. In this context, he introduced the terms "ideal" (inspired by Ernst Kummer's notion of ideal number) and "module" and
Ring_(mathematics)
Non ideal compressible fluid dynamics (NICFD), or non ideal gas dynamics, is a branch of fluid mechanics studying the dynamic behavior of fluids not obeying
Non ideal compressible fluid dynamics
Non_ideal_compressible_fluid_dynamics
Statement in abstract algebra
finite number n of vectors, and the space is therefore isomorphic to Fn. The corresponding statement with F generalized to a principal ideal domain R
Structure theorem for finitely generated modules over a principal ideal domain
Structure_theorem_for_finitely_generated_modules_over_a_principal_ideal_domain
Number in {..., –2, –1, 0, 1, 2, ...}
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations
Integer
How 435 seats are distributed to 50 states
century, the number of representatives increased every decade as more states joined the union, and the population increased. The ideal number of members
United States congressional apportionment
United_States_congressional_apportionment
Algebraic structure
in a number field) any ideal (such as the one generated by 6) decomposes uniquely as a product of prime ideals. Any maximal ideal is a prime ideal or,
Commutative_ring
Number equal to the sum of its proper divisors
it is called τέλειος ἀριθμός (téleios arithmós; 'perfect', 'ideal', or 'complete number'). Euclid also proved a formation rule (Book IX, Proposition
Perfect_number
Concept of the ideally slim female body
The thin ideal is the concept of the ideally slim female body. The common perception of this ideal is a woman who possesses a slender, feminine physique
Thin_ideal
Algebraic structure
principal ideal domain, or PID, is an integral domain (that is, a non-zero commutative ring without nonzero zero divisors) in which every ideal is principal
Principal_ideal_domain
2012 Italian film
The Ideal City (Italian: La città ideale) is a 2012 Italian thriller drama film, written and directed by Luigi Lo Cascio. It is Cascio's directorial debut
The_Ideal_City
travel, tourism, insurance
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travel, tourism, insurance