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On max-flat and max-cotorsion modules

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Abstract

In this paper, we continue to study and investigate the homological objects related to s-pure and neat exact sequences of modules and module homomorphisms. A right module A is called max-flat if \({\text {Tor}}_{1}^{R}(A, R/I)= 0\) for any maximal left ideal I of R. A right module B is said to be max-cotorsion if \({\text {Ext}}^{1}_{R}(A,B)=0\) for any max-flat right module A. We characterize some classes of rings such as perfect rings, max-injective rings, SF rings and max-hereditary rings by max-flat and max-cotorsion modules. We prove that every right module has a max-flat cover and max-cotorsion envelope. We show that a left perfect right max-injective ring R is QF if and only if maximal right ideals of R are finitely generated. The max-flat dimensions of modules and rings are studied in terms of right derived functors of \(-\otimes -\). Finally, we study the modules that are injective and flat relative to s-pure exact sequences.

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  1. Yusuf Alagöz

    Present address: Department of Mathematics, Siirt University, Siirt, Turkey

Authors and Affiliations

  1. Department of Mathematics, Izmir Institute of Technology, İzmir, Turkey

    Yusuf Alagöz & Engin Büyükaşık

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  1. Yusuf Alagöz
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  2. Engin Büyükaşık
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Correspondence to Yusuf Alagöz.

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Alagöz, Y., Büyükaşık, E. On max-flat and max-cotorsion modules. AAECC 32, 195–215 (2021). https://doi.org/10.1007/s00200-020-00482-4

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  • DOI: https://doi.org/10.1007/s00200-020-00482-4

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