Finite complete rewriting systems for regular semigroups

  • Authors:
  • R. Gray;A. Malheiro

  • Affiliations:
  • Centro de Álgebra da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal;Centro de Álgebra da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal and Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova ...

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2011

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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.