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...

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...

is a free monoid. Transition monoids and syntactic monoids are used in describing finite-state machines. Trace monoids and history monoids provide a foundation...

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...

Coxeter groups – then the group ring becomes a filtered algebra. Group algebra of a locally compact group Monoid ring Kaplansky's conjectures Group representation...

rigs are rings without negative elements. (Akin to using rng to mean a ring without a multiplicative identity.) The term dioid (for "double monoid") has...

the analogous case of groups) it may be called an abelian semigroup. A monoid is an algebraic structure intermediate between semigroups and groups, and...

noncommutative rings are given by rings of square matrices or more generally by rings of endomorphisms of abelian groups or modules, and by monoid rings. Representation...

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...

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...

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...

groups) or over Mon (the category of monoids). Specifically, there are forgetful functors A : Ring → Ab M : Ring → Mon which "forget" multiplication and...

rings Quotient ring Matrix ring Endomorphism ring Polynomial ring Formal power series Monoid ring, Group ring Localization of a ring Tensor algebra Symmetric...

follows that the set of all endomorphisms of X forms a monoid, the full transformation monoid, and denoted End(X) (or EndC(X) to emphasize the category...

In mathematics, a Noetherian ring is a ring that satisfies the ascending chain condition on left and right ideals; if the chain condition is satisfied...

commutative monoids. Therefore, is it possible to define A ∞ {\displaystyle A_{\infty }} -ring spectra and E ∞ {\displaystyle E_{\infty }} -ring spectra as...

consisting of square matrices with entries in formal variables. monoid A monoid ring. Morita Two rings are said to be Morita equivalent if the category of modules...

right adjoint to F. From monoids and groups to rings. The integral monoid ring construction gives a functor from monoids to rings. This functor is left adjoint...

algebra of a monoid is a generalization of the monoid ring that allows for infinite sums of elements of a ring. Suppose that S is a monoid with the property...

associative algebras and non-associative algebras. Given an integer n, the ring of real square matrices of order n is an example of an associative algebra...

generalized to any monoid object ⁠ ( R , ⊗ ) {\displaystyle (R,\otimes )} ⁠, where R {\displaystyle R} is the object where the monoid structure has been...

If it includes the identity function, it is a monoid, called a transformation (or composition) monoid. This is the semigroup analogue of a permutation...

the category of algebras over commutative ring R, take R[N] → R[Z], where R[G] is the monoid ring of the monoid G and the morphism is induced by the inclusion...

endowed with the above product is a commutative semigroup and in fact a monoid: the identity element is the fractional ideal R. For any fractional ideal...

sense to speak of the quotient monoid M / (ker f). The first isomorphism theorem for monoids states that this quotient monoid is naturally isomorphic to the...

integral domain is a ring for which the set of nonzero elements is a commutative monoid under multiplication (because a monoid must be closed under multiplication)...

In abstract algebra, a branch of mathematics, an affine monoid is a commutative monoid that is finitely generated, and is isomorphic to a submonoid of...

A ring is a monoid for ring multiplication. In this case, the invertible elements are also called units and form the group of units of the ring. If...

can linearly extend the monoid homomorphisms  fi : M → k to k-algebra homomorphisms Fi : k[M] → k, where k[M] is the monoid ring of M over k. Then, by linearity...

algebraic structure is a monoid, usually called the full linear monoid, but occasionally also full linear semigroup, general linear monoid etc. It is actually...