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Proper left type-A monoids revisited

Published online by Cambridge University Press:  18 May 2009

John Fountain  and
Gracinda M. S. Gomes
John Fountain
Affiliation:
Dept. Mathematics, Univ. York Heslington, York YO15DD, England
Gracinda M. S. Gomes
Affiliation:
Dep. Matemática, Univ. Lisboa Rua Ernesto De Vasconcelos, Bloco C1 1700 Lisboa, Portugal
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The relation ℛ* is defined on a semigroup S by the rule that ℛ*b if and only if the elements a, b of S are related by the Green's relation ℛ in some oversemigroup of S. A semigroup S is an E-semigroup if its set E(S)of idempotents is a subsemilattice of S. A left adequate semigroup is an E-semigroup in which every ℛ*-class contains an idempotent. It is easy to see that, in fact, each ℛ*-class of a left adequate semigroup contains a unique idempotent [2]. We denote the idempotent in the ℛ*-class of a by a+.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 35 , Issue 3 , September 1993 , pp. 293 - 306
Copyright
Copyright © Glasgow Mathematical Journal Trust 1993

References

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