countably generated module

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• Countably generated — In mathematics, the term countably generated can have several meanings: An algebraic structure (group, module, algebra) having countably many generators, see generating set (disambiguation) Countably generated space, a topological space in which… …   Wikipedia

• Finitely-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… …   Wikipedia

• Finitely generated module — In mathematics, a finitely generated module is a module that has a finite generating set. Equivalently, it is a homomorphic image of a free module on finitely many generators. The kernel of this homomorphism need not be finitely generated (then… …   Wikipedia

• Projective module — In mathematics, particularly in abstract algebra and homological algebra, the concept of projective module over a ring R is a more flexible generalisation of the idea of a free module (that is, a module with basis vectors). Various equivalent… …   Wikipedia

• Finitely generated algebra — In mathematics, a finitely generated algebra is an associative algebra A over a field K such that every element of A can be expressed as a polynomial in a finite set of elements a 1, hellip;, a n of A , with coefficients in K . If it is necessary …   Wikipedia

• Hilbert C*-module — Hilbert C* modules are mathematical objects which generalise the notion of a Hilbert space (which itself is a generalisation of Euclidean space), in that they endow a linear space with an inner product which takes values in a C* algebra. Hilbert… …   Wikipedia

• List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia

• Cardinal function — In mathematics, a cardinal function (or cardinal invariant) is a function that returns cardinal numbers. Contents 1 Cardinal functions in set theory 2 Cardinal functions in topology 2.1 Basic inequalities …   Wikipedia

• Linear algebra — R3 is a vector (linear) space, and lines and planes passing through the origin are vector subspaces in R3. Subspaces are a common object of study in linear algebra. Linear algebra is a branch of mathematics that studies vector spaces, also called …   Wikipedia

• KK-theory — This article is on the generalization of operator K theory and K homology. For the epistemological concept, see KK principle. In mathematics, KK theory is a common generalization both of topological K homology and K theory (more precisely… …   Wikipedia

• Sheaf (mathematics) — This article is about sheaves on topological spaces. For sheaves on a site see Grothendieck topology and Topos. In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.… …   Wikipedia