homological elements
71Exact sequence — In mathematics, especially in homological algebra and other applications of abelian category theory, as well as in differential geometry and group theory, an exact sequence is a (finite or infinite) sequence of objects and morphisms between them… …
72Axiomatic system — In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A mathematical theory consists of an axiomatic system and all its derived theorems. An axiomatic… …
73Multilinear algebra — In mathematics, multilinear algebra extends the methods of linear algebra. Just as linear algebra is built on the concept of a vector and develops the theory of vector spaces, multilinear algebra builds on the concepts of p vectors and… …
74Ring theory — In abstract algebra, ring theory is the study of rings algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers. Ring theory studies the structure of rings, their… …
75Algebraic K-theory — In mathematics, algebraic K theory is an important part of homological algebra concerned with defining and applying a sequence Kn(R) of functors from rings to abelian groups, for all integers n. For historical reasons, the lower K groups K0 and… …
76Künneth theorem — In mathematics, especially in homological algebra and algebraic topology, a Künneth theorem is a statement relating the homology of two objects to the homology of their product. The classical statement of the Künneth theorem relates the singular… …
77Geometric group theory — is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act (that is, when the… …
78Galois cohomology — In mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups. A Galois group G associated to a field extension L / K acts in a natural way… …
79Schur multiplier — In mathematical group theory, the Schur multiplier or Schur multiplicator is the second homology group of a group G. It was introduced by Issai Schur (1904) in his work on projective representations. Contents 1 Examples and properties 2 Re …
80Injective sheaf — In mathematics, injective sheaves of abelian groups are used to construct the resolutions needed to define sheaf cohomology (and other derived functors, such as sheaf Ext .). There is a further group of related concepts applied to sheaves: flabby …
