# 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 ).
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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