Characterizing cogenerating and finitely cogenerated S-acts

In this paper, we introduce cogenerating classes of S-acts as those that can be used to cogenerate S-acts in an appropriate sense. Next, finitely cogenerated S-acts are characterized by the property that their socle is finitely cogenerated and large in the S-act. Further, we investigate the S-acts cogenerating S_S, or  generating the injective envelope E(S) of S_S.  This leads us to introduce the classes of  cofaithful and subgenerator S-acts as thedual notions of faithful S-acts, which  lie strictly between the classes of generator and faithful S-acts. Ultimately, we study relations between the cogenerating classes, finitely cogenerated S-acts, and the recently introduced new classes of S-acts.

کلیدواژه ها:

S-acts ، cogenerator ، subgenerator ، finitely cogenerated ، cofaithful