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arXiv · 1003.4028

An elegant 3-basis for inverse semigroups

Joao Araujo·Michael Kinyon
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Abstract

It is well known that in every inverse semigroup the binary operation and the unary operation of inversion satisfy the following three identities: [\quad x=(xx')x \qquad \quad (xx')(y'y)=(y'y)(xx') \qquad \quad (xy)z=x(yz"). ] The goal of this note is to prove the converse, that is, we prove that an algebra of type $<2,1>$ satisfying these three identities is an inverse semigroup and the unary operation coincides with the usual inversion on such semigroups.

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Joao Araujo, Michael Kinyon. 2010-07-28. An elegant 3-basis for inverse semigroups. https://arxiv.org/abs/1003.4028

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