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Strongly injective modules

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Abstract

Let R be a ring with identity and M be a left R-module. The module M is called strongly injective if whenever \(M+K=N\) with \(M\subseteq N\), there exists a submodule \(K^{'}\) of K such that \(M\oplus K^{'}=N\). In this paper, we provide the various properties of the class of these modules. In particular, we prove that M is strongly injective if and only if it is semisimple injective. Moreover, we give new characterizations of semisimple rings and left V-rings via strongly injective modules. Finally, we show that every strongly injective module is strongly noncosingular.

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Authors and Affiliations

  1. Faculty of Art and Science, Department of Mathematics, Amasya University, Ipekköy, Amasya, Turkey

    Ergül Türkmen & Burcu Nişancı Türkmen

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  1. Ergül Türkmen
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  2. Burcu Nişancı Türkmen
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Correspondence to Burcu Nişancı Türkmen.

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Türkmen, E., Türkmen, B.N. Strongly injective modules. Rend. Circ. Mat. Palermo, II. Ser 70, 1–7 (2021). https://doi.org/10.1007/s12215-019-00479-0

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