A 2-base for inverse semigroups
Group Theory
2012-10-12 v1
Abstract
An open problem in the theory of inverse semigroups was whether the variety of such semigroups, when viewed as algebras with a binary operation and a unary operation, is 2-based, that is, has a base for its identities consisting of 2 independent axioms. In this note, we announce the affirmative solution to this problem: the identities form a base for inverse semigroups where turns out to be the natural inverse operation. We recount here the history of the problem including our previous efforts to find a 2-base using automated deduction and the method that finally worked. We describe our efforts to simplify the proof using \textsc{Prover9}, present the simplified proof itself and conclude with some open problems.
Cite
@article{arxiv.1210.3285,
title = {A 2-base for inverse semigroups},
author = {Joao Araujo and Michael Kinyon and R. Padmanabhan},
journal= {arXiv preprint arXiv:1210.3285},
year = {2012}
}