Relative $C$-$(n,m)$-cotorsion modules

Document Type : Research Paper

Authors

Department of Mathematics, Payame Noor University, Tehran, ‎Iran

Abstract

‎Let $R$ be a ring‎, ‎$C$ a (faithfully) semidualizing module‎, ‎and $n‎, ‎m \geq 0$ be integers or potentially $n = \infty$‎. ‎We introduce and analyze $C$-(n,m)-cotorsion modules‎, ‎utilizing the class of $R$-modules with $C$-$FP_n$-flat dimensions at most $m$ as a broad generalization‎. ‎This framework provides a new classification of $C$-cotorsion and $C$-$m$-weak cotorsion modules‎, ‎along with their equivalent characterizations‎. ‎Furthermore‎, ‎we examine the Foxby equivalences between subclasses of the Auslander and Bass classes with respect to $C$‎. ‎Lastly‎, ‎we explore the properties of strongly $C$-$(n,m)$-cotorsion dimensions in the context of almost excellent extensions‎, ‎considering the class of $R$-modules with $C$-$FP_n$-flat (or injective) dimensions at most $m$‎.

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Main Subjects

References

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Journal of Mahani Mathematical Research
Volume 15, Issue 1 - Serial Number 33
January 2026
Pages 523-543

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History

  • Receive Date: 25 June 2025
  • Revise Date: 04 October 2025
  • Accept Date: 07 December 2025

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