Please use this identifier to cite or link to this item:
https://hdl.handle.net/11147/7821
Title: | Max-Projective Modules | Authors: | Alagöz, Yusuf Büyükaşık, Engin |
Keywords: | Injective modules Max-projective modules Rings (Algebra) R -projective modules |
Publisher: | World Scientific Publishing | 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. | URI: | https://doi.org/10.1142/S021949882150095X https://hdl.handle.net/11147/7821 |
ISSN: | 0219-4988 1793-6829 |
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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10.1142@S021949882150095X.pdf | 400.87 kB | Adobe PDF | View/Open |
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