more specifically in homological algebra, a resolution (or left resolution; dually a coresolution or right resolution) is an exact sequence of modules...

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

Year's Day Dispute resolution, the settlement of a disagreement Resolution (algebra), an exact sequence in homological algebra Resolution (logic), a rule...

In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, which is a non-singular variety...

lemma Extension (algebra) Central extension Splitting lemma Projective module Injective module Projective resolution Injective resolution Koszul complex...

In homological algebra, a branch of mathematics, a matrix factorization is a tool used to study infinitely long resolutions, generally over commutative...

the bar resolution, bar construction, standard resolution, or standard complex, is a way of constructing resolutions in homological algebra. It was first...

Vieta, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to his innovative use of letters as parameters...

example of a Koszul algebra is a polynomial ring over a field, for which the Koszul complex is the minimal graded free resolution of the ground field...

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...

In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over...

In algebra, flat modules include free modules, projective modules, and, over a principal ideal domain, torsion-free modules. Formally, a module M over...

Springer resolution is a resolution of the variety of nilpotent elements in a semisimple Lie algebra, or the unipotent elements of a reductive algebraic group...

In homological algebra, the Cartan–Eilenberg resolution is in a sense, a resolution of a chain complex. It can be used to construct hyper-derived functors...

glossary of commutative algebra. See also list of algebraic geometry topics, glossary of classical algebraic geometry, glossary of algebraic geometry, glossary...

In algebraic geometry, the homogeneous coordinate ring is a certain commutative ring assigned to any projective variety. If V is an algebraic variety given...

Let π : Y → X {\displaystyle \pi :Y\to X} be a morphism between complex algebraic varieties, where Y {\displaystyle Y} is smooth and carries a symplectic...

predicts that the gonality of the algebraic curve C can be calculated by homological algebra means, from a minimal resolution of an invertible sheaf of high...

mathematics, real algebraic geometry is the sub-branch of algebraic geometry studying real algebraic sets, i.e. real-number solutions to algebraic equations with...

projective resolution of singularities X ′ → X {\displaystyle X'\to X} . Despite Chow's theorem, not every complex analytic variety is a complex algebraic variety...

homological algebra, in which ideas from algebraic topology are used to construct invariants of algebraic structures. The homology of groups, Lie algebras, and...

In Boolean algebra, the consensus theorem or rule of consensus is the identity: x y ∨ x ¯ z ∨ y z = x y ∨ x ¯ z {\displaystyle xy\vee {\bar {x}}z\vee...

In algebraic geometry, the Bott–Samelson resolution of a Schubert variety is a resolution of singularities. It was introduced by Bott & Samelson (1958)...

The Godement resolution of a sheaf is a construction in homological algebra that allows one to view global, cohomological information about the sheaf in...

normalization lemma Resolution of singularities Eisenbud, D. Commutative Algebra (1995). Springer, Berlin. Theorem 11.5 Eisenbud, D. Commutative Algebra (1995). Springer...

In algebraic geometry, a crepant resolution of a singularity is a resolution that does not affect the canonical class of the manifold. The term "crepant"...

In commutative algebra, a quasi-excellent ring is a Noetherian commutative ring that behaves well with respect to the operation of completion, and is...

mathematics, injective sheaves of abelian groups are used to construct the resolutions needed to define sheaf cohomology (and other derived functors, such as...

field of an algebraic variety Ample line bundle Ample vector bundle Linear system of divisors Birational geometry Blowing up Resolution of singularities...

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