Abstract
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).
Publisher
Cambridge University Press (CUP)
Reference11 articles.
1. A representation of a semigroup by a semigroup of matrices over a group with zero
2. (7) Fountain J. B. , Abundant semigroups. Proc. London Math. Soc., to appear.
3. (3) El-Qallalj A. and Fountain J. B. , Proper right type A monoids, in preparation.
4. One-to-one partial right translations of a right cancellative semigroup
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