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A characterization of adequate semigroups by forbidden subsemigroups

Published online by Cambridge University Press:  03 December 2013

João Araújo ,
Michael Kinyon  and
António Malheiro
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)
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Abstract

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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
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 6 , December 2013 , pp. 1115 - 1122
Copyright
Copyright © Royal Society of Edinburgh 2013