algebra, a monoid ring is a ring constructed from a ring and a monoid, just as a group ring is constructed from a ring and a group. Let R be a ring and let...
4 KB (585 words) - 12:13, 11 June 2024
coordinate ring.) The above definitions have been generalized to rings graded using any monoid G as an index set. A G-graded ring R is a ring with a direct...
16 KB (2,821 words) - 20:02, 17 August 2024
is a free monoid. Transition monoids and syntactic monoids are used in describing finite-state machines. Trace monoids and history monoids provide a foundation...
35 KB (4,447 words) - 08:24, 16 July 2024
noncommuting variables with coefficients in the ring R is the monoid ring R[N], where the monoid N is the free monoid on n letters, also known as the set of all...
51 KB (8,173 words) - 20:35, 14 June 2024
In mathematics, the plactic monoid is the monoid of all words in the alphabet of positive integers modulo Knuth equivalence. Its elements can be identified...
9 KB (1,043 words) - 00:26, 24 April 2024
Semiring (redirect from Idempotent semi-ring)
arises as the function composition of endomorphisms over any commutative monoid. Some authors call semiring the structure without the requirement for there...
52 KB (8,051 words) - 01:50, 26 June 2024
Semigroup (redirect from Monoid theory)
the analogous case of groups) it may be called an abelian semigroup. A monoid is an algebraic structure intermediate between semigroups and groups, and...
37 KB (4,675 words) - 07:50, 7 June 2024
In category theory, a branch of mathematics, a monoid (or monoid object, or internal monoid, or algebra) (M, μ, η) in a monoidal category (C, ⊗, I) is...
5 KB (511 words) - 14:20, 31 January 2024
Stanley–Reisner ring was used to characterize the numbers of faces in each dimension of simplicial polytopes. Every ring can be thought of as a monoid in Ab, the...
99 KB (13,632 words) - 06:07, 27 August 2024
Coxeter groups – then the group ring becomes a filtered algebra. Group algebra of a locally compact group Monoid ring Kaplansky's conjectures Group representation...
21 KB (3,985 words) - 12:37, 31 May 2024