Finite complete rewriting systems for regular semigroups

R. Gray; A. Malheiro

doi:10.1016/j.tcs.2010.10.020

Finite complete rewriting systems for regular semigroups

R. Gray^*, A. Malheiro

^*Corresponding author for this work

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

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. (C) 2010 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	654-661
Number of pages	8
Journal	Theoretical Computer Science
Volume	412
Issue number	8-10
DOIs	https://doi.org/10.1016/j.tcs.2010.10.020
Publication status	Published - 4 Mar 2011

Keywords

Rewriting systems
Finitely presented groups and semigroups
Finite complete rewriting systems
Regular semigroups
Ideal extensions
Completely 0-simple semigroups
MONOIDS
SUBGROUPS
PRESENTATIONS

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10.1016/j.tcs.2010.10.020

Finiteness Conditions and Index: Finiteness Conditions and Index in Semigroups and Monoids
Gray, R. D. (PI)
EPSRC
1/02/08 → 31/01/11
Project: Standard

Cite this

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title = "Finite complete rewriting systems for regular semigroups",

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. (C) 2010 Elsevier B.V. All rights reserved.",

keywords = "Rewriting systems, Finitely presented groups and semigroups, Finite complete rewriting systems, Regular semigroups, Ideal extensions, Completely 0-simple semigroups, MONOIDS, SUBGROUPS, PRESENTATIONS",

author = "R. Gray and A. Malheiro",

year = "2011",

month = mar,

day = "4",

doi = "10.1016/j.tcs.2010.10.020",

language = "English",

volume = "412",

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journal = "Theoretical Computer Science",

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TY - JOUR

T1 - Finite complete rewriting systems for regular semigroups

AU - Gray, R.

AU - Malheiro, A.

PY - 2011/3/4

Y1 - 2011/3/4

N2 - 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.

AB - 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.

KW - Rewriting systems

KW - Finitely presented groups and semigroups

KW - Finite complete rewriting systems

KW - Regular semigroups

KW - Ideal extensions

KW - Completely 0-simple semigroups

KW - MONOIDS

KW - SUBGROUPS

KW - PRESENTATIONS

U2 - 10.1016/j.tcs.2010.10.020

DO - 10.1016/j.tcs.2010.10.020

M3 - Article

SN - 0304-3975

VL - 412

SP - 654

EP - 661

JO - Theoretical Computer Science

JF - Theoretical Computer Science

IS - 8-10

ER -

Finite complete rewriting systems for regular semigroups

Abstract

Keywords

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Projects

Finiteness Conditions and Index: Finiteness Conditions and Index in Semigroups and Monoids

Cite this