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Factorisable right adequate semigroups

Published online by Cambridge University Press:  20 January 2009

Abdulsalam El-Qallali
Abdulsalam El-Qallali
Affiliation:
Department of Mathematics, Al-Fateh University, Tripoli, S.P.L.A.J. (Libya)
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On a semigroup S the relation ℒ* is defined by the rule that (a, b) ∈ ℒ* if and only if the elements a, b of S are related by Green's relation ℒ in some oversemigroup of S. It is well known that for a monoid S, every principal right ideal is projective if and only if each ℒ*-class of S contains an idempotent. Following (6) we say that a semigroup with or without an identity in which each ℒ*-class contains an idempotent and the idempotents commute is right adequate. A right adequate semigroup S in which eS ∩ aS = eaS for any e2 = e, a ∈ S is called right type A. This class of semigroups is studied in (5).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 24 , Issue 3 , October 1981 , pp. 171 - 178
Copyright
Copyright © Edinburgh Mathematical Society 1981

References

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