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

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.

Downloads

Published

2025-10-10

Issue

Contemporary Mathematics, Volume 6 Issue 5 (2025)

Section

Research Article

License

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