The Generalizations Of Injective S-acts And Regular S-acts

In this paper,we investigate the generalizations of injective S-acts.By using the properties of INC-injective S-acts,C-injective S-acts and CC-injective S-acts,we give some characterizations of monoids,and obtain some equivalent characteri-zations of monoids over which all fgdu-weakly injective right S-acts are regular.It is an open question to characterize monoids over which all regular acts are weakly injective acts.On this issue,some examples are given to prove that it is wrong to some conclusions in this paper.