An elegant 3-basis for inverse semigroups
Group Theory
2012-10-01 v3
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 satisfying these three identities is an inverse semigroup and the unary operation coincides with the usual inversion on such semigroups.
Keywords
Cite
@article{arxiv.1003.4028,
title = {An elegant 3-basis for inverse semigroups},
author = {Joao Araujo and Michael Kinyon},
journal= {arXiv preprint arXiv:1003.4028},
year = {2012}
}
Comments
4 pages; v.2: fixed abstract; v.3: final version with minor changes suggested by referee, to appear in Semigroup Forum