Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/11449
Title: On max-flat and max-cotorsion modules
Authors: Alagöz, Yusuf
Büyükaşık, Engin
Keywords: (Max-)flat modules
Max-cotorsion modules
SP-flat modules
Max-hereditary rings
Quasi-Frobenius rings
Issue Date: 2021
Publisher: Springer
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 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 Ext(R)(1)(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 -circle times-. Finally, we study the modules that are injective and flat relative to s-pure exact sequences.
URI: https://doi.org/10.1007/s00200-020-00482-4
https://hdl.handle.net/11147/11449
ISSN: 0938-1279
1432-0622
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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