Finite complete rewriting systems for regular semigroups
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. (C) 2010 Elsevier B.V. All rights reserved.
finite complete rewriting systems rewriting systems regular semigroups ideal extensions completely 0-simple semigroups finitely presented groups and semigroups