On fully dense acts [Articol]

Abstract

Over a monoid S fully dense S-acts as a generalization of monoids for which any right ideal is a generator are introduced and investigated. First some general properties on fully dense S-acts are mentioned and then monoids over which all free (projective) S-acts are fully dense are characterized. Moreover the relation between these kinds of S-acts and some other classes of S-acts such as prime and strongly prime S-acts is studied.