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 | |
| 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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Dive into the research topics of 'Finite complete rewriting systems for regular semigroups'. Together they form a unique fingerprint.Projects
- 1 Finished
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Finiteness Conditions and Index: Finiteness Conditions and Index in Semigroups and Monoids
Gray, R. (PI)
1/02/08 → 31/01/11
Project: Standard
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