pure injective group

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• 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

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• Pure subgroup — In mathematics, especially in the area of algebra studying the theory of abelian groups, a pure subgroup is a generalization of direct summand. It has found many uses in abelian group theory and related areas.DefinitionA subgroup S of a… …   Wikipedia

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• Abelian group — For other uses, see Abelian (disambiguation). Abelian group is also an archaic name for the symplectic group Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product,… …   Wikipedia

• Algebraically compact group — In mathematics, in the realm of Abelian group theory, a group is said to be algebraically compact if it is a direct summand of every Abelian group containing it as a pure subgroup.Equivalent characterizations of algebraic compactness: * The group …   Wikipedia

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• Algebraically compact module — In mathematics, especially in the area of abstract algebra known as module theory, algebraically compact modules, also called pure injective modules, are modules that have a certain nice property which allows the solution of infinite systems of… …   Wikipedia

• Bass–Serre theory — is a part of the mathematical subject of group theory that deals with analyzing the algebraic structure of groups acting by automorphisms on simplicial trees. The theory relates group actions on trees with decomposing groups as iterated… …   Wikipedia

• Universal coefficient theorem — In mathematics, the universal coefficient theorem in algebraic topology establishes the relationship in homology theory between the integral homology of a topological space X, and its homology with coefficients in any abelian group A. It states… …   Wikipedia