Browsing by Author "Turkmen, Burcu Nisanci"

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Citation - WoS: 1
Citation - Scopus: 2
On a Class of Harada Rings
(De Gruyter Poland Sp. z o.o., 2022) Turkmen, Burcu Nisanci; Demirci, Yilmaz Mehmet; 01. Abdullah Gül University; 02.01. Mühendislik Bilimleri; 02. Mühendislik Fakültesi
In this study, inspired by the definition and a previous study [F. Eryilmaz, SS -lifting modules and rings, Miskolc Math. Notes 22 (2021), no. 2, 655-662], left Harada rings are adapted to ss-Harada rings, and the important properties of these rings are provided. The characterization of a left ss-Harada ring R with R left perfect and Rad(R) included in Soc(RR) was found with the help of strongly local R-modules.
Citation - WoS: 2
Citation - Scopus: 2
On Rings With One Middle Class of Injectivity Domains
(Univ Osijek, dept Mathematics, 2022) Alizade, Rafail; Demirci, Yilmaz Mehmet; Turkmen, Burcu Nisanci; Turkmen, Ergul; 01. Abdullah Gül University; 02.01. Mühendislik Bilimleri; 02. Mühendislik Fakültesi
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.
Citation - WoS: 5
Citation - Scopus: 5
Rings With Modules Having a Restricted Injectivity Domain
(Springer International Publishing AG, 2020) Demirci, Yilmaz Mehmet; Turkmen, Burcu Nisanci; Turkmen, Ergul; 01. Abdullah Gül University; 02.01. Mühendislik Bilimleri; 02. Mühendislik Fakültesi
We introduce modules whose injectivity domains are contained in the class of modules with zero radical and call them working-class. This notion gives a generalization of poor modules that have minimal injectivity domain. Semisimple working-class modules always exist for arbitrary rings whereas their predecessors do not. We investigate the rings over which every module is either injective or working-class. Right weakly V-rings are examples of these rings. Moreover, we study the existence of working-class simple modules and show that if there is a projective working-class simple right module, then the ring is a right GV-ring.