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...

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

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...

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...

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

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...

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

arises as the function composition of endomorphisms over any commutative monoid. Some authors call semiring the structure without the requirement for there...

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...

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

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...

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

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...

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...

Deitmar's notions by "gluing" the category of multiplicative monoids and the category of rings to create a new category M R , {\displaystyle {\mathfrak {M}}{\mathfrak...

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...

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...

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...

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...

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...

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

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...

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...

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)...

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...

X_{2}X_{3}X_{1}^{4}X_{4}} . The non-commutative polynomial ring may be identified with the monoid ring over R of the free monoid of all finite words in the Xi. Since the...