On Finite Semigroup Cross-Sections and Complete Rewriting Systems
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 pa...
| Main Author: | |
|---|---|
| Format: | conferenceObject |
| Language: | eng |
| Published: |
2019
|
| Subjects: | |
| Online Access: | http://www.scopus.com/record/display.uri?eid=2-s2.0-84878137901&origin=resultslist&sort=plf-f&src=s&st1 |
| Country: | Portugal |
| Oai: | oai:run.unl.pt:10362/65920 |
| Summary: | 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. |
|---|