monoid

(redirected from Monoids)

monoid

[′mä‚nȯid]
(mathematics)
A semigroup which has an identity element.

monoid

An operator * and a value x form a monoid if * is associative and x is its left and right identity.
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digital representations of real numbers), and for recognizing some sets of integers or more generally of finitely generated abelian groups or monoids.
Negatively ordered semigroups and monoids arise naturally in various semigroup theoretic contexts; see, for example, [3,4,11].
Sincesticker systems with finite sets of axioms and sticker rules generate only regular languages-without restrictions [5], monoids [6] and permutation groups [7] had been associated to generate more powerful languages than regular languages.
The topics include Kostka systems and exotic t-structures for reflection groups, quantum deformations of irreducible representations of GL(mn) toward the Kronecker problem, generic extensions and composition monoids of cyclic quivers, blocks of truncated q-Schur algebras of type A, a survey of equivariant map algebras with open problems, and forced gradings and the Humphrey-Verma conjecture.
This theory was later extended by Brown [11, 12] to a larger class of monoids called left regular bands.
He is the co-inventor of three additional patents in the areas of multistream encryption systems, high-speed cryptography, and cryptographically secure algebraic key establishment protocols based on monoids.
The structure theory of symplectic rook monoids was studied by Li and Renner using elementary matrices (see [4] for more details).
A powerful technical tool for classifying regular languages and proving decidability results is Eilenberg-Reiterman theory, which assigns classes of finite monoids or single profinite algebras to classes of languages.
Naturally, in order to say that set partitions act on abelian Hopf monoids, we need to define the notion of ring in species.
Topics include opf monoids and split extensions of Hopf algebras, the double crossed product of weak Hopf algebras, recovering information from character tables of Hopf algebras, hom-quasi-bialgebras, the green rings of the generalized Taft Hopf algebras, and Morita equivalence methods in classification of fusion categories.
Since the 1970s a number of results have appeared on generalizing the Morita theory of rings with identity to monoids [4,10], associative rings [1,3,8] or semigroups [7,15,19].
It was proved in [11] that a semigroup S is an C-wrpp semigroup if and only if S is a strong semilattice of R-left cancellative monoids.