homological elements
11Adjoint functors — Adjunction redirects here. For the construction in field theory, see Adjunction (field theory). For the construction in topology, see Adjunction space. In mathematics, adjoint functors are pairs of functors which stand in a particular… …
12List of commutative algebra topics — Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative… …
13Torsion (algebra) — In abstract algebra, the term torsion refers to a number of concepts related to elements of finite order in groups and to the failure of modules to be free. Definition Let G be a group. An element g of G is called a torsion element if g has… …
14Snake lemma — The snake lemma is a tool used in 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 and its applications, for instance …
15Cartan, Henri — ▪ 2009 Henri Paul Cartan French mathematician born July 8, 1904, Nancy, France died Aug. 13, 2008, Paris, France made fundamental advances in the theory of analytic functions. Cartan was also a founding member of the secretive group of… …
16Ronald Brown (mathematician) — Ronald Brown, MA, D.Phil Oxon, FIMA, Emeritus Professor (born January 4, 1935) is an English mathematician. He is best known for his many, substantial contributions to Higher Dimensional Algebra and non Abelian Algebraic Topology, involving… …
17Alexander Grothendieck — User:Geometry guy/InfoboxAlexander Grothendieck (born March 28, 1928 in Berlin, Germany) is considered to be one of the greatest mathematicians of the 20th century. He made major contributions to: algebraic topology, algebraic geometry, number… …
18Homology — may refer to:* Homology (anthropology), analogy between human beliefs, practices or artifacts due to genetic or historical connections. * Homology (biology): similar structures due to shared ancestry. * Homology (chemistry): a compound of a… …
19Projective module — In mathematics, particularly in abstract algebra and homological algebra, the concept of projective module over a ring R is a more flexible generalisation of the idea of a free module (that is, a module with basis vectors). Various equivalent… …
20Derived functor — In mathematics, certain functors may be derived to obtain other functors closely related to the original ones. This operation, while fairly abstract, unifies a number of constructions throughout mathematics. Contents 1 Motivation 2 Construction… …
