Free right type A semigroups

Fountain, John

Glasgow mathematical journal, Tome 33 (1991) no. 2, pp. 135-148

Résumé

The relation L* is defined on a semigroup S by the rule that a L*b if and only if the elements a, b of S are related by Green's relation L 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 right adequate semigroup is an E-semigroup in which every L*-class contains an idempotent. It is easy to see that, in fact, each L*-class of a right adequate semigroup contains a unique idempotent [8]. We denote the idempotent in the L*-class of a by a*. Then we may regard a right adequate semigroup as an algebra with a binary operation of multiplication and a unary operation *. We will refer to such algebras as *-semigroups. In [10], it is observed that viewed in this way the class of right adequate semigroups is a quasi-variety.

Détail

DOI : 10.1017/S0017089500008168

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