Characterizing cogenerating and finitely cogenerated $S$-acts

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Sciences, Fasa University, Fasa, Iran.

2 Department of Mathematics, Shaanxi University of Science and Technology, Xi$'$an, Shaanxi, P.R. China.

3 College of Engineering, Lamerd Higher Education Center, Shiraz University of Technology, Lamerd, Iran.

10.48308/cgasa.2024.235961.1497

Abstract

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 the
dual 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.

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References

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Categories and General Algebraic Structures with Applications

Articles in Press, Accepted Manuscript
Available Online from 15 September 2024

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