This analysis reveals when cyclic modules are cocyclic and the conditions for embedding in free modules.
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.
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Alvarado-García et al. (2025) studied this question.
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