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* Every [[monoid]] is a semigroup, by "forgetting" the identity element.

| [[monoid]] | [[monoid]]

== Matrix monoid <math>\mathit{SO}(\mathbb{Z}_+, 2)</math> == ...Furthermore,&nbsp; <math>\mathit{SO}(\mathbb{Z}_+, 2)</math>&nbsp; is a [[monoid]] with respect to the matrix multiplication.

...ing classes of fuzzy subalgebras. In such a case a fuzzy subset ''s'' of a monoid (M,•,'''u''') is a fuzzy submonoid if and only if

...',·) is ''not'' a group. The most we can say is that it is a commutative [[monoid]]. ...minate the requirement that every element have an inverse, then we get a [[monoid]].

...or multiplication say that '''Z''' under multiplication is a [[commutative monoid]]. However, note that not every integer has a multiplicative inverse; e.g.

...For instance, they can be defined as the [[convolution algebra]] of the [[monoid]] of non-negative powers of the generator ''X'' of a cyclic group. This me