Finite complete rewriting systems for regular semigroups

Details Finite complete rewriting systems for regular semigroups Finite complete rewriting systems for regular semigroups

2010-05-17

arxiv.org/abs/1005.2972v1

Mathematics

Group Theory

11 pages

Scientific paper

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.

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