# monoid

(redirected from Commutative monoid)

## 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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If (M, +,0) is a commutative monoid, then its group completion Gp(M) can be described as the quotient M x M/~, where (m, n) ~ (p, q) when there exists k [member of]m such that
If (S, [cross product], 1) is a commutative monoid then S is called a commutative semiring.
1]-ring to be a commutative monoid with an absorbing element 0.
1) is a commutative monoid and the following conditions hold for all x, y, z [member of] A,
We have shown that the set of all fuzzy interior ideals of a left regular ordered LA -semigroup with left identity forms a commutative monoid.
I] is also a commutative monoid with multiplication [*.
That is, JX is the free k-module on the commutative monoid under coproduct of isomorphism classes of objects of [epsilon](X).
a) (A, *, [less than or equal to]) is a partially ordered commutative monoid with a greatest element 1 where x [less than or equal to] y if and only if x [right arrow] y =1.
A rig (or semiring) is a ring without negatives: a set equipped with a commutative monoid structure (+, 0) and a monoid structure (x, 1), the latter distributing over the former.
This is the left regular band analogue of free partially commutative monoids (also called trace monoids or graph monoids [18, 14]) and of free partially commutative groups (also called right-angled Artin groups or graph groups [31]).
Trace monoids are obtained from free monoids by allowing certain pairs of generators to commute, which is the reason why they are also known as free partially commutative monoids.
Garcia-Sanchez, Finitely generated commutative monoids.

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