Finite complete rewriting systems for regular semigroups
Group Theory
2017-06-23 v1
Abstract
It is proved that, given a (von Neumann) regular semigroup with finitely many left and right ideals, if every maximal subgroup is presentable by a finite complete rewriting system, then so is the semigroup. To achieve this, the following two results are proved: the property of being defined by a finite complete rewriting system is preserved when taking an ideal extension by a semigroup defined by a finite complete rewriting system; a completely 0-simple semigroup with finitely many left and right ideals admits a presentation by a finite complete rewriting system provided all of its maximal subgroups do.
Cite
@article{arxiv.1005.2972,
title = {Finite complete rewriting systems for regular semigroups},
author = {Robert Gray and António Malheiro},
journal= {arXiv preprint arXiv:1005.2972},
year = {2017}
}
Comments
11 pages