@conference {DBLP:conf/tmfcs/Malheiro08, title = {On Finite Semigroup Cross-Sections and Complete Rewriting Systems}, booktitle = {International Conference on Theoretical and Mathematical Foundations of Computer Science, TMFCS-08, Orlando, Florida, USA, July 7-10, 2008}, year = {2008}, note = {

n/a

}, pages = {59{\textendash}63}, abstract = {

In this paper we obtain a [finite] complete rewriting system defining a semigroup/monoid S, from a given finite
right cross-section of a subsemigroup/submonoid defined by a [finite] complete presentation. In the semigroup case the subsemigroup must have a right identity element which must also be part of the cross-section. In the monoid case the submonoid and the cross-section must include the identity of the semigroup. The result on semigroups allow us to show that if G is a group defined by a [finite] complete rewriting system then the completely simple semigroup M[G; I, J; P] is also defined by a [finite] complete rewriting system.

}, author = {Malheiro, A.} }