Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins...

In mathematics, homological conjectures have been a focus of research activity in commutative algebra since the early 1960s. They concern a number of...

in homological algebra, a differential graded algebra is a graded associative algebra with an added chain complex structure that respects the algebra structure...

This is a list of homological algebra topics, by Wikipedia page. Cokernel Exact sequence Chain complex Differential module Five lemma Short five lemma...

right R-module M. The concept of torsion plays an important role in homological algebra. If M and N are two modules over a commutative domain R (for example...

and is a foundational part of algebraic geometry; homological algebra; Lie algebra and Lie group theory; Boolean algebra, which is widely used for the...

of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory...

In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral...

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...

In mathematics, and more specifically in homological algebra, a resolution (or left resolution; dually a coresolution or right resolution) is an exact...

In homological algebra, a monad is a 3-term complex A → B → C of objects in some abelian category whose middle term B is projective, whose first map A → B...

In mathematics, especially in homological algebra and algebraic topology, a Künneth theorem, also called a Künneth formula, is a statement relating the...

algebra homology. The exterior algebra is the main ingredient in the construction of the Koszul complex, a fundamental object in homological algebra....

Extraordinary homology theory Homological algebra Homological conjectures in commutative algebra Homological connectivity Homological dimension Homotopy group...

of the core concepts of homological algebra, in which ideas from algebraic topology are used to define invariants of algebraic structures. The cohomology...

component-free approach is also used extensively in abstract algebra and homological algebra, where tensors arise naturally. Note: This article assumes...

particularly homological algebra, to construct long exact sequences. The snake lemma is valid in every abelian category and is a crucial tool in homological algebra...

In mathematics, homotopical algebra is a collection of concepts comprising the nonabelian aspects of homological algebra, and possibly the abelian aspects...

mirror symmetry in mathematical terms. While the homological mirror symmetry is based on homological algebra, the SYZ conjecture is a geometrical realization...

the central concepts of homological algebra, in which ideas from algebraic topology are used to construct invariants of algebraic structures. The homology...

the original idea, for example the concept of perverse sheaf in homological algebra. The theory mentioned above does not directly relate to the concept...

in homological algebra, but are used in several areas of mathematics, including abstract algebra, Galois theory, differential geometry and algebraic geometry...

p-adic integers. Combinatorial commutative algebra Invariant theory Serre's multiplicity conjectures Homological conjectures Commutative ring Module (mathematics)...

His research interests lay in the area of algebra, involving abelian groups, modules, homological algebra, and combinatorics. Rotman was the Managing...

flat resolutions from projective resolutions is called relative homological algebra, and is covered in classics such as Mac Lane (1963) and in more recent...

equivalence, Morita duality Category of vector spaces Homological algebra Filtration (algebra) Exact sequence Functor Zorn's lemma Semigroup Subsemigroup...

to homological algebra. Cambridge University Press. p. 240. Baez, John C.; Crans, Alissa S. (2004). "Higher-dimensional algebra VI: Lie 2-algebras". Theory...

concordance of numerical and homological equivalence, implies the equivalence of pure motives with respect to homological and numerical equivalence. (In...

abstract homological algebra, unifying previously disparate presentations of homology and cohomology for associative algebras, Lie algebras, and groups...

Mathematical Journal. It revolutionized the subject of homological algebra, a purely algebraic aspect of algebraic topology. It removed the need to distinguish...