# homological algebra

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## homological algebra

[¦hä·mə¦läj·ə·kəl ′al·jə·brə]
(mathematics)
The study of the structure of modules, particularly by means of exact sequences; it has application to the study of a topological space via its homology groups.
References in periodicals archive ?
Their topics include normal forms for vectors and univariate polynomials, twisted associative algebras and shuffle algebras, operadic homological algebra and Gr|bner bases, linear algebra over polynomial rings, and a case study of non-symmetric ternary quadratic operads.
The subject area is an innovative blend of group theory, homological algebra, topology, geometry, number theory and computer science.
Some notions of homological algebra should be recalled from [3, 13], in order to formulate the next result.
He assumes students are familiar with homological algebra, algebraic topology based on different forms, and de Rham cohomology.
We present here a synopsis of the results together with applications of this beautiful interplay between combinatorial topology and homological algebra.
This two-volume research monograph on the general Lagrangian Floer theory and the accompanying homological algebra of filtered $A_\infty$-algebras provides the most important step towards a rigorous foundation of the Fukaya category in general context.
Davis, A vanishing theorem in homological algebra, Comment.
For example, set theory was invented in order to help in analysing the convergence behaviour of Fourier series; homological algebra was invented in order to serve algebraic topology, and category theory was first developed with the view of applying it in homological algebra (as well as algebraic topology and algebraic geometry).
Lubkin introduces entirely new invariants in homological algebra and commutative and even non-commutative algebra that have never been considered before.
Positselski, Homological algebra of semimodules and semicontramodules.
Some familiarity with basic homological algebra is needed in the final chapter.

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