Browsing by Author "Demirci, Yilmaz Mehmet"

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Closures of proper classes
(University of Miskolc matronto@uni-miskolc.hu, 2016) Refail Alizade; Yılmaz Mehmet Demirci; Alizade, Rafail; Demirci, Yilmaz Mehmet
For an integral domain R we consider the closures M (Mr r ε R) of a submodule M of an R-module N consisting of elements n of N with tn 2 M (rmn ε M) for some nonzero t ε R (m ε Z+) and its connections with usual closure M of M in N. Using these closures we study the closures P and Pr of a proper class P of short exact sequences and give a decomposition for the class of quasi-splitting short exact sequences of abelian groups into the direct sum of "p-closures" of the class Split of splitting short exact sequences and description of closures of some classes. In the general case of an arbitrary ring we generalize these closures of a proper class P by means of homomorphism classes F and G and prove that under some conditions this closure is a propier classes. © 2020 Elsevier B.V. All rights reserved.
Citation - WoS: 2
Citation - Scopus: 2
On rings with one middle class of injectivity domains
(Udruga Matematicara Osijek, 2022) Refail Alizade; Yılmaz Mehmet Demirci; Burcu Nişanci Türkmen; Ergül Türkmen; Türkmen, Burcu Nişancı; Alizade, Rafail; Türkmen, Ergül; Demirci, Yilmaz Mehmet
A module M is said to be modest if the injectivity domain of M is the class of all crumbling modules. In this paper we investigate the basic properties of modest modules. We provide characterizations of some classes of rings using modest modules. In particular we show that a ring having the class of crumbling modules as the only right middle class of injectivity domains is either a right V-ring or right Noetherian, and a commutative ring with this property is regular. We also give criteria for a ring having the class of crumbling modules as the only right middle class of injectivity domains. © 2022 Elsevier B.V. All rights reserved.