In mathematics, the quasi-commutative property is an extension or generalization of the general commutative property. This property is used in specific...

commutant) Commutative diagram Commutative (neurophysiology) Commutator Particle statistics (for commutativity in physics) Quasi-commutative property Trace...

algebra, a quasi-free algebra is an associative algebra that satisfies the lifting property similar to that of a formally smooth algebra in commutative algebra...

(Gelfand–Naimark). In commutative algebraic geometry, algebraic schemes are locally prime spectra of commutative unital rings (A. Grothendieck), and every quasi-separated...

algebra is the branch of commutative algebra that studies commutative local rings and their modules. In practice, a commutative local ring often arises...

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

In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center...

allow harmonic analysis to be used in number theory. The spectrum of any commutative ring with the Zariski topology (that is, the set of all prime ideals)...

idempotent, commutative quasigroup under the operation x ∗ y = (x + y) / 2. Every Steiner triple system defines an idempotent, commutative quasigroup:...

Whether a ring is commutative (that is, its multiplication is a commutative operation) has profound implications on its properties. Commutative algebra, the...

quasi-isomorphism if the chain map on the underlying (co)chain complexes is. A commutative differential graded algebra (or CDGA) is a differential graded algebra...

alternation, transposition, interchange, bi-commutative, bisymmetric, surcommutative, entropic, etc. Any commutative semigroup is a medial magma, and a medial...

cancellation property. Magmas with commutativity Commutative magma: A magma with commutativity. Commutative monoid: A monoid with commutativity. Abelian group:...

\mathrm {soc} (_{R}R)\cong R/J} . For a commutative ring R, the following are equivalent: R is Frobenius R is quasi-Frobenius R is a finite direct sum of...

to Grothendieck describes the structure of quasi-finite morphisms of schemes. Several results in commutative algebra imply the geometric forms of Zariski's...

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...

The homomorphism comes from the universal property of localization. On an arbitrary ringed space, quasi-coherent sheaves do not necessarily form an...

operation arises as the function composition of endomorphisms over any commutative monoid. Some authors define semirings without the requirement for there...

noncommutative geometry, that studies the geometric properties of formal duals of non-commutative algebraic objects such as rings as well as geometric...

space V over a field K is a commutative algebra over K that contains V, and is, in some sense, minimal for this property. Here, "minimal" means that S(V)...

Z with morphisms to X and Z, making the diagram commutative, and which is universal with that property. That is, for any scheme W with morphisms to X and...

radicals, rings are usually assumed to be associative, but need not be commutative and need not have a multiplicative identity. In particular, every ideal...

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

In commutative algebra, the prime spectrum (or simply the spectrum) of a commutative ring R {\displaystyle R} is the set of all prime ideals of R {\displaystyle...

(k)} is proper. For any natural number n, projective space Pn over a commutative ring R is proper over R. Projective morphisms are proper, but not all...

maximal ideal m . {\displaystyle {\mathfrak {m}}.} This property is fundamental in commutative algebra and algebraic geometry, since it reduces the study...

\operatorname {GL} (A)={\text{colim}}\operatorname {GL} _{n}(A)} for a commutative ring A {\displaystyle A} , then the subgroup of elementary matrices E...

is a generic property; and the failure of flatness occurs on the jumping set of the morphism. The first of these comes from commutative algebra: subject...

In mathematics, the Grothendieck group, or group of differences, of a commutative monoid M is a certain abelian group. This abelian group is constructed...

development of algebraic geometry, and its algebraic counterpart, called commutative algebra. From the late 1950s through the mid-1970s algebraic geometry...