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

In mathematics, Serre's multiplicity conjectures, named after Jean-Pierre Serre, are certain problems in commutative algebra, motivated by the needs of...

is called commutative algebra. Complementarily, noncommutative algebra is the study of ring properties that are not specific to commutative rings. This...

Derived category Group cohomology Galois cohomology Lie algebra cohomology Sheaf cohomology Whitehead problem Homological conjectures in commutative algebra...

This is a list of notable mathematical conjectures. The following conjectures remain open. The (incomplete) column "cites" lists the number of results...

In commutative algebra, a regular local ring is a Noetherian local ring having the property that the minimal number of generators of its maximal ideal...

of the connected components of M-curves? Homological conjectures in commutative algebra Jacobson's conjecture: the intersection of all powers of the Jacobson...

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

projective under mild conditions that are generally satisfied in commutative algebra and algebraic geometry. This makes the concept of flatness useful mainly...

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

those arising from homological algebra and K-theory more frequently carry over to the noncommutative setting. Commutative algebraic geometry begins by...

figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra...

are used in conjectures on special values of L-functions and the formulation of a non-commutative main conjecture of Iwasawa theory and in construction...

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

in many parts of mathematics such as number theory, commutative algebra, and algebraic geometry. In ring theory, many classes of rings, such as unique...

including scheme theory from algebraic geometry, category theory, and homological algebra. Another example is Goldbach's conjecture, which asserts that every...

In commutative algebra, the Krull dimension of a commutative ring R, named after Wolfgang Krull, is the supremum of the lengths of all chains of prime...

In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations...

problems of algebraic geometry, such as the Weil conjectures (the last of which was proved by Pierre Deligne). Strongly based on commutative algebra, scheme...

theory) Morava K-theory Hodge conjecture Weil conjectures Directed algebraic topology Example: DE-9IM Chain complex Commutative diagram Exact sequence Five...

short exact sequences in an abelian category, as well as fiber sequences and cofiber sequences in topology. Much of homological algebra is clarified and extended...

prove two of the Weil conjectures (together with Michael Artin and Jean-Louis Verdier) by 1965. The last of the Weil conjectures (an analogue of the Riemann...

complex variables and then commutative algebra and algebraic geometry, where he introduced sheaf theory and homological algebra techniques. Serre's thesis...

algebra topics List of homological algebra topics List of group theory topics List of representation theory topics List of linear algebra topics List of reciprocity...

Derived algebraic geometry is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local charts...

In the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra...

Homological conjectures in commutative algebra "Local Cohomology and the Homological Conjectures in Commutative Algebra" (PDF). www5a.biglobe.ne.jp. Retrieved...

of div is the group of units in O, while the cokernel is the ideal class group. In the language of homological algebra, this says that there is an exact...

Homological algebra. Encyclopedia of Mathematical Sciences. Springer. Manin, Yuri; Gelfand, Sergei Gelfand (1996). Methods of Homological algebra. Springer...

Differentially closed field Differential graded algebra – Algebraic structure in homological algebra D-module – Module over a sheaf of differential operators...