Hostname: page-component-7b9c58cd5d-bslzr Total loading time: 0.001 Render date: 2025-03-15T12:27:16.106Z Has data issue: false hasContentIssue false

A characterization of adequate semigroups by forbidden subsemigroups

Published online by Cambridge University Press:  03 December 2013

João Araújo
Affiliation:
Universidade Aberta, Rua da Escola Politécnica 147, 1269-001 Lisboa, Portugal and Centro de Álgebra, Universidade de Lisboa, 1649-003 Lisboa, Portugal (mjoao@ptmat.fc.ul.pt)
Michael Kinyon
Affiliation:
Universidade Aberta, Rua da Escola Politécnica 147, 1269-001 Lisboa, Portugal and Centro de Álgebra, Universidade de Lisboa, 1649-003 Lisboa, Portugal (mjoao@ptmat.fc.ul.pt)
António Malheiro
Affiliation:
Universidade Aberta, Rua da Escola Politécnica 147, 1269-001 Lisboa, Portugal and Centro de Álgebra, Universidade de Lisboa, 1649-003 Lisboa, Portugal (mjoao@ptmat.fc.ul.pt)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A semigroup is amiable if there is exactly one idempotent in each ℛ*-class and in each ℒ*-class. A semigroup is adequate if it is amiable and if its idempotents commute. We characterize adequate semigroups by showing that they are precisely those amiable semigroups that do not contain isomorphic copies of two particular non-adequate semigroups as subsemigroups.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2013