principal ideal domain
61Finitely-generated module — In mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated R module also may be called a finite R module or finite over R.[1] Related concepts include finitely cogenerated modules, finitely… …
62Integer — This article is about the mathematical concept. For integers in computer science, see Integer (computer science). Symbol often used to denote the set of integers The integers (from the Latin integer, literally untouched , hence whole : the word… …
63Hauptideal — Das Hauptideal ist ein Begriff aus der Ringtheorie, einem Teilgebiet der Algebra. Es stellt eine Verallgemeinerung der aus der Schulmathematik bekannten Teilmengen der ganzen Zahlen dar, die Vielfache einer Zahl sind. Beispiele für solche… …
64Modular representation theory — is a branch of mathematics, and that part of representation theory that studies linear representations of finite group G over a field K of positive characteristic. As well as having applications to group theory, modular representations arise… …
65Degree of a polynomial — The degree of a polynomial represents the highest degree of a polynominal s terms (with non zero coefficient), should the polynomial be expressed in canonical form (i.e. as a sum or difference of terms). The degree of an individual term is the… …
66Krull dimension — In commutative algebra, the Krull dimension of a ring R, named after Wolfgang Krull (1899–1971), is the supremum of the number of strict inclusions in a chain of prime ideals. The Krull dimension need not be finite even for a Noetherian ring. A… …
67Global dimension — In ring theory and homological algebra, the global dimension (or global homological dimension; sometimes just called homological dimension) of a ring A denoted gl dim A , is a non negative integer or infinity which is a homological invariant of… …
68Stark–Heegner theorem — In number theory, a branch of mathematics, the Stark–Heegner theorem states precisely which quadratic imaginary number fields admit unique factorisation in their ring of integers. It solves a special case of Gauss s class number problem of… …
69Module (mathematics) — For other uses, see Module (disambiguation). In abstract algebra, the concept of a module over a ring is a generalization of the notion of vector space, wherein the corresponding scalars are allowed to lie in an arbitrary ring. Modules also… …
70Indecomposable module — In abstract algebra, a module is indecomposable if it is non zero and cannot be written as a direct sum of two non zero submodules.Indecomposable is a weaker notion than simple module:simple means no proper submodule N < M,while indecomposable… …
