Neat submodules over commutative rings

Mermut, Engin; Türkoğlu, Zübeyir

doi:10.1080/00927872.2019.1677697

Cited by 3 publications

(2 citation statements)

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“…Unlike the generation of pure submodules the notions of s-pure and neat submodules are not only inequivalent they are also incomparable. Recently, the commutative rings for which the notions of s-pure and neat submodules are equivalent are completely characterized in [18,Theorem 3.7]. These are exactly the commutative rings whose maximal ideals are finitely generated and locally principal.…”

Section: Max-flat Preenvelopes Which Are Epimorphismsmentioning

confidence: 99%

“…In [6], S. Crivei proved that if the ring is commutative and the maximal ideals are principal, then the notions s-pure and neat submodules coincide. Recently, the commutative rings with this property are completely characterized in [18,Theorem 3.7]. These are exactly the commutative rings whose maximal ideals are finitely generated and locally principal.…”

Section: Introductionmentioning

confidence: 99%

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On MF-projective modules

Alagöz

2021

Hacettepe Journal of Mathematics and Statistics

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In this paper, we study the left orthogonal class of max-flat modules which are the homological objects related to s-pure exact sequences of modules and module homomorphisms. Namely, a right module A is called MF-projective if Ext 1 R (A, B) = 0 for any max-flat right R-module B, and A is called strongly MF-projective if Ext i R (A, B) = 0 for all max-flat right R-modules B and all i ≥ 1. Firstly, we give some properties of M F-projective modules and SMF-projective modules. Then we introduce and study MF-projective dimensions for modules and rings. The relations between the introduced dimensions and other (classical) homological dimensions are discussed. We characterize some classes of rings such as perfect rings, QF rings and max-hereditary rings by (S)M F-projective modules. We also study the rings whose right ideals are MF-projective. Finally, we characterize the rings whose M F-projective modules are projective.

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Section: Max-flat Preenvelopes Which Are Epimorphismsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%