Abstract
In the present paper, we study simple-direct-injective modules and simple-direct-projective modules over a formal matrix ring \(K=\left(\begin{matrix}R&M\\ N&S\end{matrix}\right)\), where \(M\) is an \((R,S)\)-bimodule and \(N\) is a \((S,R)\)-bimodule over rings \(R\) and \(S\). We determine necessary and sufficient conditions for a \(K\)-module to be, respectively, simple-direct-injective or simple-direct-projective. We also give some examples to illustrate and delimit our results.
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Funding
A.N. Abyzov was supported by Volga Region Scientific-Educational Centre of Mathematics, project no. 075-02-2020-1478. D.T. Tapkin was supported by the Russian Science Foundation, grant no. 18-11-00028.
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(Submitted byM. M. Arslanov)
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Abyzov, A.N., Tapkin, D.T. Simple-Direct Modules Over Formal Matrix Rings. Lobachevskii J Math 42, 1–14 (2021). https://doi.org/10.1134/S1995080221010029
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DOI: https://doi.org/10.1134/S1995080221010029