homological algebra

См. также в других словарях:

• Homological algebra — is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract… …   Wikipedia

• Mapping cone (homological algebra) — In homological algebra, the mapping cone is a construction on a map of chain complexes inspired by the analogous construction in topology. In the theory of triangulated categories it is a kind of combined kernel and cokernel: if the chain… …   Wikipedia

• List of homological algebra topics — This is a list of homological algebra topics, by Wikipedia page. Basic techniques Cokernel Exact sequence Chain complex Differential module Five lemma Short five lemma Snake lemma Nine lemma Extension (algebra) Central extension Splitting lemma… …   Wikipedia

• Homological dimension — refers to a number of related concepts in homological algebra: * Global dimension, the homological dimension of a ring * Projective dimension, the homological dimension of a module * Injective dimension, the dual notion * Cohomological dimension …   Wikipedia

• Homological mirror symmetry — is a mathematical conjecture made by Maxim Kontsevich. It seeks a systematic mathematical explanation for a phenomenon called mirror symmetry first observed by physicists studying string theory.In an address to the 1994 International Congress of… …   Wikipedia

• Álgebra homológica — El álgebra homológica es un campo de las matemáticas que estudia la homología en un marco algebraico general. Es una disciplina relativamente joven, cuyos orígenes pueden remontarse a investigaciones en topología combinatoria (un precursor de la… …   Wikipedia Español

• homological — adjective Date: circa 1847 1. homologous 2. of or relating to topological homology theory < homological algebra > • homologically adverb …   New Collegiate Dictionary

• Homological conjectures in commutative algebra — In mathematics, the homological conjectures have been a focus of research activity in commutative algebra since the early 1960s. They concern a number of interrelated (sometimes surprisingly so) conjectures relating various homological properties …   Wikipedia

• List of commutative algebra topics — Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative… …   Wikipedia

• Lie algebra cohomology — In mathematics, Lie algebra cohomology is a cohomology theory for Lie algebras. It was defined by Chevalley and Eilenberg (1948) in order to give an algebraic construction of the cohomology of the underlying topological spaces of compact Lie …   Wikipedia

• Torsion (algebra) — In abstract algebra, the term torsion refers to a number of concepts related to elements of finite order in groups and to the failure of modules to be free. Definition Let G be a group. An element g of G is called a torsion element if g has… …   Wikipedia