A Note on Left Cocyclic Modules

Authors

  • Alejandro Alvarado-García Faculty of Sciences, National Autonomous University of Mexico, Exterior Circuit, C.U., Mexico City, Postal Code 04510, Mexico
  • C´esar Cejudo-Castilla Faculty of Physico-Mathematical Sciences, Benemérita Autonomous University of Puebla, Av. San Claudio & 18 Sur, Col. San Manuel, University City, Puebla, Postal Code 72570, Mexico
  • Tania Gabriela Pérez-Quijano Faculty of Physico-Mathematical Sciences, Benemérita Autonomous University of Puebla, Av. San Claudio & 18 Sur, Col. San Manuel, University City, Puebla, Postal Code 72570, Mexico
  • Ivan Fernando Vilchis-Montalvo Faculty of Physico-Mathematical Sciences, Benemérita Autonomous University of Puebla, Av. San Claudio & 18 Sur, Col. San Manuel, University City, Puebla, Postal Code 72570, Mexico https://orcid.org/0000-0001-8082-6969 (unauthenticated)

DOI:

https://doi.org/10.37256/cm.6520256497

Keywords:

cyclic module, cocyclic module, artinian principal ideal rings, left uniserial ring, left Köthe ring

Abstract

We explore some properties of cocyclic modules and rings. We establish when every cyclic module is cocyclic. In addition, we characterize the case in which every cocyclic module embeds in a free module. Finally, we give the necessary conditions for a class of cocyclic modules to be closed under quotients and projective covers.

References

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Published

2025-10-10

Issue

Contemporary Mathematics, Volume 6 Issue 5 (2025), 5368-7533

Section

Research Article

License

Copyright (c) 2025 Ivan Fernando Vilchis-Montalvo, et al.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

1.
A Note on Left Cocyclic Modules. Contemp. Math. [Internet]. 2025 Oct. 10 [cited 2025 Dec. 24];6(5):7422-31. Available from: https://ojs353.mebyme.cn/index.php/CM/article/view/6497