Fundamental theorem of ideal theory in number fields information

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...

theorem of Galois theory Fundamental theorem of geometric calculus Fundamental theorem on homomorphisms Fundamental theorem of ideal theory in number...

In mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every...

structure of the unit group of quadratic fields, he proved the Dirichlet unit theorem, a fundamental result in algebraic number theory. He first used the pigeonhole...

meaningless to decide which field a particular result belongs to. For example, Hilbert's Nullstellensatz is a theorem which is fundamental for algebraic geometry...

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...

In number theory, the ideal class group (or class group) of an algebraic number field K is the quotient group JK /PK where JK is the group of fractional...

In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions...

In algebraic number theory, a quadratic field is an algebraic number field of degree two over Q {\displaystyle \mathbf {Q} } , the rational numbers. Every...

element of a PID has a unique decomposition into prime elements (so an analogue of the fundamental theorem of arithmetic holds); any two elements of a PID...

in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater...

{Q} } . The fundamental theorem of Galois theory links fields in between K {\displaystyle K} and its algebraic closure and closed subgroups of Gal(K). For...

set theory. For instance, the development of the fundamentals of model theory (such as the compactness theorem) rely on the axiom of choice, and is in fact...

defined on number fields and their field extensions. Connes embedding problem in Von Neumann algebra theory Crouzeix's conjecture: the matrix norm of a complex...

applied fields. Contents:  Top 0–9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 2-factor theorem (graph theory) 15 and 290 theorems (number theory) 2π...

intersection of finitely many primary ideals. The Lasker–Noether theorem, given here, may be seen as a certain generalization of the fundamental theorem of arithmetic:...

extension field of the real numbers; the real numbers are a subfield of the complex numbers. Field extensions are fundamental in algebraic number theory, and...

Finite fields are fundamental in a number of areas of mathematics and computer science, including number theory, algebraic geometry, Galois theory, finite...

polynomial equation with rational coefficients), in both qualitative and quantitative ways. The fundamental theorem of algebra tells us that if we have a non-constant...

concept of an abelian group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theory of abelian...

In 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...

der Waerden himself on ideals as the main references. The three isomorphism theorems, called homomorphism theorem, and two laws of isomorphism when applied...

generalization of the fundamental theorem of finitely generated abelian groups and roughly states that finitely generated modules over a principal ideal domain...

function of K, and the analytic class number formula for K. A theorem of Hermite states that there are only finitely many number fields of bounded discriminant...