WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7150
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Article Citation - WoS: 8Citation - Scopus: 9Max-Projective Modules(World Scientific Publishing, 2020) Alagöz, Yusuf; Büyükaşık, EnginWeakening 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.Article Citation - WoS: 1Citation - Scopus: 1Strongly Noncosingular Modules(Iranian Mathematical Society, 2016) Alagöz, Yusuf; Durğun, YılmazAn R-module M is called strongly noncosingular if it has no nonzero Rad-small (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingular R-modules; (3) absolutely coneat modules are strongly noncosingular if and only if R is a right max ring and injective modules are strongly noncosingular; (4) a commutative ring R is semisimple if and only if the class of injective modules coincides with the class of strongly noncosingular R-modules.