monoid


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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 for each group H such that the monoids End(G) and End(H) are isomorphic implies an isomorphism between G and H, we say that the group G is determined by its endomorphism monoid in the class of all groups.
8 The structure {GI, x) is a monoid under the operation(aI)(bI) = abI for all a, b in the group (G, x) and [I.
member of] I(X) is the neutral element with respect to the composition, moreover, this inverse monoid also has a zero element which is the empty map previously defined.
The set A* together with concatenation forms a free monoid with the neutral element [epsilon].
If (S, [cross product], 1) is a commutative monoid then S is called a commutative semiring.
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.
the free monoid (1) generated by [SIGMA] with the concatenation as the internal operation and s as the neutral element.
a] : a [member of] A} of M by open sets indexed by a set A, a schedule is an element of the monoid SA = [(A x [R.
m] is a monoid (semigroup with an identity) under composition of partial transformations, usually called the symmetric inverse semigroup on m letters.