On finite complete rewriting systems and large subsemigroups

K. B. Wong; P. C. Wong

On finite complete rewriting systems and large subsemigroups

Group Theory 2011-08-23 v2

Authors: K. B. Wong , P. C. Wong

Abstract

Let $S$ be a semigroup and $T$ be a subsemigroup of finite index in $S$ (that is, the set $S\setminus T$ is finite). The subsemigroup $T$ is also called a large subsemigroup of $S$ . It is well known that if $T$ has a finite complete rewriting system then so does $S$ . In this paper, we will prove the converse, that is, if $S$ has a finite complete rewriting system then so does $T$ . Our proof is purely combinatorial and also constructive.

Keywords

finite group theory semigroup theory

Cite

@article{arxiv.1005.0882,
  title  = {On finite complete rewriting systems and large subsemigroups},
  author = {K. B. Wong and P. C. Wong},
  journal= {arXiv preprint arXiv:1005.0882},
  year   = {2011}
}

Comments

We have made major changes to the paper and simplified most of the proofs

On finite complete rewriting systems and large subsemigroups

Abstract

Keywords

Cite

Comments

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