Sequentially pure injectivity

AuthorsH.Barzegar
JournalQuaestiones Mathematicae
Page number191-201
Serial number2
Volume number38
Paper TypeOriginal Research
Published At2015
Journal GradeScientific - research
Journal TypeTypographic
Journal CountrySouth Africa

Abstract

Injectivity with respect to pure monomorphisms was studied before in
categories of modules and categories of acts. In this paper we study this notion with
respect to sequentially pure monomorphisms.
Although the Baer criterion for injectivity (weakly injectivity implies 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 fact, we are not aware of any type of weak
injectivity implying injectivity of S-acts, in general, other than the Skornjakov-Baer
criterion, which says that injectivity with respect to subacts of cyclic acts implies
injectivity with respect to all monomorphisms.
M.M. Ebrahimi and M. Mahmoudi in some papers have shown this criterion to be
true for some special S.