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

In abstract algebra, the free monoid on a set is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from that...

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

computer science, the syntactic monoid M ( L ) {\displaystyle M(L)} of a formal language L {\displaystyle L} is the minimal monoid that recognizes the language...

topological monoid is a monoid object in the category of topological spaces. In other words, it is a monoid with a topology with respect to which the monoid's binary...

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...

In abstract 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...

the set of nonnegative integers or the set of integers, but can be any monoid. The direct sum decomposition is usually referred to as gradation or grading...

A Cartesian monoid is a monoid, with additional structure of pairing and projection operators. It was first formulated by Dana Scott and Joachim Lambek...

Look up monoid in Wiktionary, the free dictionary. A monoid is an algebraic structure. Monoid may also refer to: Monoid (category theory), a mathematical...

In algebra, a presentation of a monoid (or a presentation of a semigroup) is a description of a monoid (or a semigroup) in terms of a set Σ of generators...

monoids were first presented by M.W. Shields. History monoids are isomorphic to trace monoids (free partially commutative monoids) and to the monoid of...

complete equivalence under all reorderings. The trace monoid or free partially commutative monoid is a monoid of traces. Traces were introduced by Pierre Cartier...

multiplicative monoids called the structure sheaf. An affine monoid scheme is a monoidal space that is isomorphic to the spectrum of a monoid, and a monoid scheme...

Any monoid can be understood as a special sort of category (with a single object whose self-morphisms are represented by the elements of the monoid), and...

important special case is a monoid action or act, in which the semigroup is a monoid and the identity element of the monoid acts as the identity transformation...

In abstract algebra, an additive monoid ( M , 0 , + ) {\displaystyle (M,0,+)} is said to be zerosumfree, conical, centerless or positive if nonzero elements...

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...

coincides with the presentation of a monoid. Thus they constitute a natural framework for solving the word problem for monoids and groups. An SRS can be defined...

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...

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...

the structures are the same, and the resulting magma is a commutative monoid. This can then be used to prove the commutativity of the higher homotopy...

a monoid, one can still use the notion of a generating set S {\displaystyle S} of G {\displaystyle G} . S {\displaystyle S} is a semigroup/monoid generating...

positive integer n such that xn = xn+1. An aperiodic monoid is an aperiodic semigroup which is a monoid. A finite semigroup is aperiodic if and only if it...

certain commutative monoids that are not groups. A commutative monoid on which a monus operator is defined is called a commutative monoid with monus, or CMM...

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

Associated with any semiautomaton is a monoid called the characteristic monoid, input monoid, transition monoid or transition system of the semiautomaton...

category theory, a (strict) n-monoid is an n-category with only one 0-cell. In particular, a 1-monoid is a monoid and a 2-monoid is a strict monoidal category...

category may also be viewed as a "categorification" of an underlying monoid, namely the monoid whose elements are the isomorphism classes of the category's objects...

In mathematics, the Chinese monoid is a monoid generated by a totally ordered alphabet with the relations cba = cab = bca for every a ≤ b ≤ c. An algorithm...