Abstract
Given modules M and A, M is said to be A–RD–subinjective 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 RD–subinjectivity domain of M is defined to be the collection of all modules A such that M is A–RD-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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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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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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DOI: https://doi.org/10.1007/s12215-024-01089-1