E-local pseudovarieties

Moura, Ana

http://hdl.handle.net/10400.22/11162

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Authors

Moura, Ana

Abstract(s)

Generalizingapropertyofthepseudovarietyofallaperiodicsemi- groups observed by Tilson, we call E-local a pseudovariety V which satisfies the following property: for a finite semigroup, the subsemigroup generated by its idempotents belongs to V if and only if so do the subsemigroups generated by the idempotents in each of its regular D-classes. In this paper, we present sev- eral sufficient or necessary conditions for a pseudovariety to be E-local or for a pseudoidentity to define an E-local pseudovariety. We also determine several examples of the smallest E-local pseudovariety containing a given pseudovariety.