Malheiro, António José Mesquita da Cunha Machado2019-04-082019-04-082008-01-01978-1-60651-006-3PURE: 407911PURE UUID: 8373022c-77a3-4b44-a361-dc87ccfd1db3researchoutputwizard: 21815Scopus: 84878137901ORCID: /0000-0003-1186-6216/work/63724731http://www.scopus.com/record/display.uri?eid=2-s2.0-84878137901&origin=resultslist&sort=plf-f&src=s&st1In 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.5105501engRewriting systemsSemigroupsIdentity elementsSemi-groupconference objecthttps://www.scopus.com/pages/publications/84878137901