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Max-projective modules

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info:eu-repo/semantics/closedAccess

Date

2020

Author

Alagöz, Yusuf
Büyükaşık, Engin

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Abstract

Weakening the notion of R-projectivity, a right R-module M is called max-projective provided that each homomorphism f: M ? R/I, where I is any maximal right ideal, factors through the canonical projection : R ? R/I. We study and investigate properties of max-projective modules. Several classes of rings whose injective modules are R-projective (respectively, max-projective) are characterized. For a commutative Noetherian ring R, we prove that injective modules are R-projective if and only if R = A × B, where A is QF and B is a small ring. If R is right hereditary and right Noetherian then, injective right modules are max-projective if and only if R = S × T, where S is a semisimple Artinian and T is a right small ring. If R is right hereditary then, injective right modules are max-projective if and only if each injective simple right module is projective. Over a right perfect ring max-projective modules are projective. We discuss the existence of non-perfect rings whose max-projective right modules are projective. © 2020 World Scientific Publishing Company.

Source

Journal of Algebra and its Applications

URI

https://doi.org/10.1142/S021949882150095X
https://hdl.handle.net/11147/7821

Collections

  • Mathematics / Matematik [691]
  • Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection [4673]



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