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<math> (\mathbb N,+) </math> is a semigroup with neutral element 0. It is: <math> (\mathbb N \setminus\{0\},\cdot) </math> is a semigroup with neutral element 1. It is:

...xioms define other useful algebraic structures — e.g., [[groupoid]]s and [[semigroup]]s. * If we additionally do not require an identity either, then we get a [[semigroup]].

* {{cite book | author=John M. Howie | title=Fundamentals of Semigroup Theory | publisher=[[Oxford University Press]] | year=1995 | isbn=0-19-8511

*20Mxx [[Semigroup]]s