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Some Results of Fully Prime Submodules

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Abstract

A fully invariant submodule \(N\) of \(M\) is called fully prime in \(M\) if for fully invariant submodules \(K\) and \(L\) of \(M\), \(K*_{M}L\leq N\) implies \(K\leq N\) or \(L\leq N\) with \(K*_{M}L=\textrm{Hom}(M,K)L\) [11]. In this paper, we give some characterizations of fully prime submodules. We, among other results, show that every fully prime submodule of a self-generator right \(R\)-module contains a minimal fully prime submodule. We also study the endomorphisms ring of fully prime modules. We show that the endomorphisms ring of fully prime quasi-projective modules are prime.

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ACKNOWLEDGMENTS

The author would like to thank the referees for the very helpful comments and suggestions.

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Authors and Affiliations

  1. The Vietnam National Institute of Educational Sciences (VNIES), No 101, Tran Hung Dao, Hoan Kiem, Ha Noi, Vietnam

    Dinh Duc Tai

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  1. Dinh Duc Tai
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Correspondence to Dinh Duc Tai.

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(Submitted by I. Sh. Kalimullin)

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Tai, D.D. Some Results of Fully Prime Submodules. Lobachevskii J Math 43, 2301–2308 (2022). https://doi.org/10.1134/S1995080222110282

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  • DOI: https://doi.org/10.1134/S1995080222110282

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