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...
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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...
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is a free monoid. Transition monoids and syntactic monoids are used in describing finite-state machines. Trace monoids and history monoids provide a foundation...
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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...
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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...
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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...
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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...
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Coxeter groups – then the group ring becomes a filtered algebra. Group algebra of a locally compact group Monoid ring Kaplansky's conjectures Group representation...
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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...
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rings Quotient ring Matrix ring Endomorphism ring Polynomial ring Formal power series Monoid ring, Group ring Localization of a ring Tensor algebra Symmetric...
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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...
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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...
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groups) or over Mon (the category of monoids). Specifically, there are forgetful functors A : Ring → Ab M : Ring → Mon which "forget" multiplication and...
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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...
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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...
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commutative monoids. Therefore, is it possible to define A ∞ {\displaystyle A_{\infty }} -ring spectra and E ∞ {\displaystyle E_{\infty }} -ring spectra as...
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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...
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Endomorphism (redirect from Endomorphism monoid)
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...
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Field with one element (section Monoid schemes)
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...
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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...
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Inverse element (redirect from Inverse (ring theory))
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...
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Dedekind domain (redirect from Dedekind ring)
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...
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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...
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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...
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generalized to any monoid object ( R , ⊗ ) {\displaystyle (R,\otimes )} , where R {\displaystyle R} is the object where the monoid structure has been...
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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...
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Algebra over a field (redirect from Algebra over a commutative ring)
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...
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Integral domain (redirect from Integral ring)
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)...
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Kernel (algebra) (redirect from Kernel (ring theory))
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...
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Free algebra (redirect from Free ring)
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...
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