An elegant 3-basis for inverse semigroups

Details An elegant 3-basis for inverse semigroups An elegant 3-basis for inverse semigroups

2010-03-21

arxiv.org/abs/1003.4028v3

Mathematics

Group Theory

4 pages; v.2: fixed abstract; v.3: final version with minor changes suggested by referee, to appear in Semigroup Forum

Scientific paper

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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