exact module

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• Module plat — La notion de module plat a été introduite par Jean Pierre Serre[1]. Elle généralise les modules projectifs et a fortiori les modules libres. En algèbre commutative et en géométrie algébrique, cette notion a été notamment exploitée par Alexander… …   Wikipédia en Français

• Module projectif — En mathématiques, un module projectif est un module P (à gauche par exemple) sur un anneau A tel que pour tout morphisme surjectif f : N → M entre deux A modules (à gauche) et pour tout morphisme g : P → M, il existe un morphisme… …   Wikipédia en Français

• Module injectif — En mathématiques, un module injectif est un module Q (à gauche par exemple) sur un anneau A tel que pour tout morphisme injectif f : X → Y entre deux A modules (à gauche) et pour tout morphisme g : X → Q, il existe un morphisme h  …   Wikipédia en Français

• Exact functor — In homological algebra, an exact functor is a functor, from some category to another, which preserves exact sequences. Exact functors are very convenient in algebraic calculations, roughly speaking because they can be applied to presentations of… …   Wikipedia

• Module (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… …   Wikipedia

• Flat module — In abstract algebra, a flat module over a ring R is an R module M such that taking the tensor product over R with M preserves exact sequences.Vector spaces over a field are flat modules. Free modules, or more generally projective modules, are… …   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

• Injective module — In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z module Q of all rational numbers. Specifically, if Q is a submodule of some… …   Wikipedia

• D-module — In mathematics, a D module is a module over a ring D of differential operators. The major interest of such D modules is as an approach to the theory of linear partial differential equations. Since around 1970, D module theory has been built up,… …   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

• Verma module — Verma modules, named after Daya Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics. The definition of a Verma module looks complicated, but Verma modules are very natural objects, with useful properties …   Wikipedia