Sequentially Complete S-acts and Baer type criteria over semigroups

Abstract

Although the Baer Criterion for injectivity is true for modules over a ring with an identity, it is an open
problem for acts over a semigroup S (with or without identity). In this work, we study a kind of Baer
Criterion for injectivity of acts over a semigroup S. We consider a kind of weak injectivity which we
call s -completeness and give some conditions under which s-completeness coincides with injectivity