Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Citation - WoS: 8Citation - Scopus: 9Max-Projective Modules(World Scientific Publishing, 2020) Alagöz, Yusuf; Alagöz, Yusuf; Büyükaşık, Engin; Büyükaşık, Engin; 01. Izmir Institute of Technology; 04.02. Department of Mathematics; 04. Faculty of ScienceWeakening 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 On pseudo semisimple rings(World Scientific Publishing Co. Pte Ltd, 2013) Büyükaşık, Engin; Mohamed, Saad H.; Büyükaşık, Engin; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyA necessary and sufficient condition is obtained for a right pseudo semisimple ring to be left pseudo semisimple. It is proved that a right pseudo semisimple ring is an internal exchange ring. It is also proved that a right and left pseudo semisimple ring is an SSP ringArticle Citation - WoS: 7Citation - Scopus: 7Strongly Radical Supplemented Modules(Springer Verlag, 2012) Büyükaşık, Engin; Büyükaşık, Engin; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyZöschinger studied modules whose radicals have supplements and called these modules radical supplemented. Motivated by this, we call a module strongly radical supplemented (briefly srs) if every submodule containing the radical has a supplement. We prove that every (finitely generated) left module is an srs-module if and only if the ring is left (semi)perfect. Over a local Dedekind domain, srs-modules and radical supplemented modules coincide. Over a nonlocal Dedekind domain, an srs-module is the sum of its torsion submodule and the radical submodule. © 2012 Springer Science+Business Media, IncArticle Citation - WoS: 16Citation - Scopus: 14Rings Whose Modules Are Weakly Supplemented Are Perfect. Applications To Certain Ring Extensions(Mathematica Scandinavica, 2009) Büyükaşık, Engin; Büyükaşık, Engin; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyIn this note we show that a ring R is left perfect if and only if every left R-module is weakly supplemented if and only if R is semilocal and the radical of the countably infinite free left R-module has a weak supplement.