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projective module

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  • 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

  • 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

  • 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

  • Projective object — In category theory, the notion of a projective object generalizes the notion of free module.An object P in a category C is projective if the hom functor: operatorname{Hom}(P, )colonmathcal{C} omathbf{Set}preserves epimorphisms. That is, every… …   Wikipedia

  • Projective cover — In category theory, a projective cover of an object X is in a sense the best approximation of X by a projective object P . Projective covers are the dual of injective envelopes. Definition Let mathcal{C} be a category and X an object in… …   Wikipedia

  • Projective space — In mathematics a projective space is a set of elements constructed from a vector space such that a distinct element of the projective space consists of all non zero vectors which are equal up to a multiplication by a non zero scalar. A formal… …   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

  • 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

  • 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

  • Galois module — In mathematics, a Galois module is a G module where G is the Galois group of some extension of fields. The term Galois representation is frequently used when the G module is a vector space over a field or a free module over a ring, but can also… …   Wikipedia

  • Fake projective plane — For Freedman s example of a non smoothable manifold with the same homotopy type as the complex projective plane, see 4 manifold. In mathematics, a fake projective plane (or Mumford surface) is one of the 50 complex algebraic surfaces that have… …   Wikipedia

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