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...

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...

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

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...

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

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

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

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...

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

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

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...

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...

least 3. In 1964, Hironaka proved that singularities of algebraic varieties admit resolutions in characteristic zero. Hironaka was able to give a general...

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

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

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

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...

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

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

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...

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

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...

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

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"...

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