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

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

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

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

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

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

(not only algebraic ones). At its origin, it was introduced, together with homological algebra for allowing the algebraic study of non-algebraic objects...

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...

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

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

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

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

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

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...

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

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

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

refer to any other concept of dimension that is defined in terms of homological algebra, which includes: Projective dimension of a module, based on projective...

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

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

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

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

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

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

central notions of commutative algebra and homological algebra, and are used widely in algebraic geometry and algebraic topology. In a vector space, the...

mathematician who co-founded category theory (with Saunders Mac Lane) and homological algebra. He was born in Warsaw, Kingdom of Poland to a Jewish family. He...

early result of homological algebra. It is the starting point of the use of homological methods in commutative algebra and algebraic geometry. The syzygy...

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