Translation for 'homological algebra' from English to Russian

homological algebra

гомологическая алгебра {ж}мат.

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algebra

алгебра {ж}мат.

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linear algebra

линейная алгебра {ж}мат.наука

abstract algebra

абстрактная алгебра {ж}мат.

• Grothendieck moved to Lawrence, Kansas at the beginning of 1955, and there he set his old subject aside in order to work in algebraic topology and homological algebra, and increasingly in algebraic geometry.
• Homological algebra is the branch of mathematics that studies homology in a general algebraic setting.
• Chain complexes are studied in homological algebra, but are used in several areas of mathematics, including abstract algebra, Galois theory, differential geometry and algebraic geometry.
• In mathematics, especially homological algebra and other applications of abelian category theory, the short five lemma is a special case of the five lemma.
• The snake lemma is a tool used in mathematics, particularly homological algebra, to construct long exact sequences.

• In homological algebra, the relationship between currying and uncurrying is known as tensor-hom adjunction.
• Category theory was originally introduced for the need of homological algebra, and widely extended for the need of modern algebraic geometry (scheme theory).
• Enter Alexander Grothendieck, who used category theory to take compass bearings in other work—in functional analysis, homological algebra and finally algebraic geometry.
• Abelian categories are the most general setting for homological algebra.
• In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations.

• A Dedekind domain can also be characterized in terms of homological algebra: an integral domain is a Dedekind domain if and only if it is a hereditary ring; that is, every submodule of a projective module over it is projective.
• Several deeper aspects of commutative rings have been studied using methods from homological algebra. [...] lists some open questions in this area of active research.
• At its origin, it was introduced, together with homological algebra for allowing the algebraic study of non-algebraic objects such as topological spaces; this particular area of application is called algebraic topology.