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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1) is a commutative monoid and the following conditions hold for all x, y, z [member of] A,
I] is also a commutative monoid with multiplication [*.
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.