rd-subinjectivity-domain-of-modules-–-springer

Rd-Subinjectivity domain of modules – Springer

Abstract

Given modules M and A, M is said to be ARDsubinjective if for every RD-extension B of A, every (fin textrm{Hom}(A, M)) extends to (textrm{Hom}(B, M)). For a module M, the RDsubinjectivity domain of M is defined to be the collection of all modules A such that M is ARD-subinjective. We investigate basic properties of RD-subinjectivity domains and provide characterizations for various types of rings and modules including p-injective modules, RD-coflat modules, von Neumann regular rings, RD-rings, Köthe rings, right Noetherian rings, and quasi-Frobenius rings in terms of RD-subinjectivity domains. Finally, we study the properties of RD-indigent modules and consider the structure of rings over which every (resp. simple) right module is RD-injective or RD-indigent.

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Acknowledgements

The authors would like to thank the anonymous referees for carefully checking the details and for helpful comments that improved this paper.

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Authors and Affiliations

  1. Department of Science, Shahreza Campus, University of Isfahan, Isfahan, Iran

    Ali Moradzadeh-Dehkordi

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. BOX: 19395-5746, Tehran, Iran

    Ali Moradzadeh-Dehkordi

  3. Department of Mathematics, Hatay Mustafa Kemal University, Hatay, Turkey

    Yusuf Alagöz

Corresponding author

Correspondence to Ali Moradzadeh-Dehkordi.

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The research of the first author was in part supported by a grant from IPM (No. 1403160411). This research is partially carried out in the IPM-Isfahan Branch.

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Moradzadeh-Dehkordi, A., Alagöz, Y. Rd-Subinjectivity domain of modules. Rend. Circ. Mat. Palermo, II. Ser (2024). https://doi.org/10.1007/s12215-024-01089-1

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