Browsing by Author "Celikel, Ece Yetkin"
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1absorbing primary submodules
Celikel, Ece Yetkin (OVIDIUS UNIV PRESS, 2021)Let R be a commutative ring with nonzero identity and M be a unitary Rmodule. The goal of this paper is to extend the concept of 1absorbing primary ideals to 1absorbing primary submodules. A proper submodule N of M is ... 
A new generalızatıon of (m, n)closed ıdeals
Khashan, Hani A.; Celikel, Ece Yetkin (Springer, 2023)Let R be a commutative ring with identity. For positive integers m and n, Anderson and Badawi (Journal of Algebra and Its Applications 16(1):1750013 (21 pp), 2017) defined an ideal I of a ring R to be an (m,n)closed if ... 
On graded jideals over graded rings
AlShorman, Tamem; Bataineh, Malik; Celikel, Ece Yetkin (KOREAN MATHEMATICAL SOC, 2023). The goal of this article is to present the graded Jideals of Ggraded rings which are extensions of Jideals of commutative rings. A graded ideal P of a Ggraded ring R is a graded Jideal if whenever x, y & ISIN; h(R), ... 
On nonnilSNoetherian and nonniluSNoetherian rings
Mahdou, Najib; Oubouhou, El Houssaine; Celikel, Ece Yetkin (Sciendo, 1 April 20)Let R be a commutative ring with identity, and let S be a multiplicative subset of R. Then R is called a nonnilSNoetherian ring if every nonnil ideal of R is Sfinite. Also, R is called a uSNoetherian ring if there ... 
On S2Prime Ideals Of Commutative Rings
Yavuz, Sanem; Ersoy, Bayram Ali; Tekir, Unsal; Celikel, Ece Yetkin (Mdpi, JUN 2024)Prime ideals and their generalizations are crucial in numerous research areas, particularly in commutative algebra. The concept of generalization of prime ideals begins with the study of weakly prime ideals. Since then, ... 
On sclean and snılclean rıngs
EsSaidi, Mohamed; Celikel, Ece Yetkin (Jangjeon Research Institute for Mathematical Sciences and Physics, 2024)Let A be a commutative ring with identity. An element a G A is said to be Sclean (resp., Snilclean), where S ⊂ A is a given multiplicative set, if there exists s ∈ S such that sa is clean (resp.. nilclean). The ring A ... 
On weakly 1Absorbing primary ıdeals of commutative rings
Badawi, Ayman; Celikel, Ece Yetkin (WORLD SCIENTIFIC PUBL CO PTE LTD, JUN 2022)Let R be a commutative ring with 1 not equal 0. We introduce the concept of weakly 1absorbing primary ideal, which is a generalization of 1absorbing primary ideal. A proper ideal I of R is said to be weakly 1absorbing ... 
On weakly Sprimary ideals of commutative rings
Celikel, Ece Yetkin; Khashan, Hani A. (WORLD SCIENTIFIC PUBL CO PTE LTD, APR 2023)Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. The purpose of this paper is to introduce the concept of weakly Sprimary ideals as a new generalization of weakly primary ideals. ... 
On weakly Sprimary submodules
Celikel, Ece Yetkin; Khashan, Hani A. (UNIV NIS, 2023)Let R be a commutative ring with a nonzero identity, S be a multiplicatively closed subset of R and M be a unital Rmodule. In this paper, we define a submodule N of M with (N :R M) n S = 0 to be weakly Sprimary if there ... 
Prime ideal sum graph of a commutative ring
Saha, Manideepa; Das, Angsuman; Celikel, Ece Yetkin; Abdioglu, Cihat (World Scıentıfıc Publ Co Pte Ltd, JUN 2023)Let R be a commutative ring with identity. The prime ideal sum graph of R, denoted by PIS(R), is a graph whose vertices are nonzero proper ideals of R and two distinct vertices I and J are adjacent if and only if I J is a ... 
Quasi Jideals of commutative rings
Khashan, Hani A.; Celikel, Ece Yetkin (SPRINGERVERLAG ITALIA SRL, JUN 2022)Let R be a commutative ring with identity. In this paper, we introduce the concept of quasi Jideal which is a generalization of Jideal. A proper ideal of R is called a quasi Jideal if its radical is a Jideal. Many ... 
QuasiSprimary ideals of commutative rings
Celikel, Ece Yetkin; Hamed, Ahmed (TAYLOR & FRANCIS INC, OCT 3 2023)Let R be a commutative ring with 1 not equal 0 and S be a multiplicatively closed subset of R. We call an ideal I of R disjoint with S quasiSprimary if there exists an s is an element of S such that whenever a, b is an ... 
Semi rideals of commutative rings
Khashan, Hani A.; Celikel, Ece Yetkin (OVIDIUS UNIV PRESS, MAR 1 2023)For commutative rings with identity, we introduce and study the concept of semi rideals which is a kind of generalization of both rideals and semiprime ideals. A proper ideal I of a commutative ring R is called semi ... 
Weakly JIdeals of Commutative Rings
Khashan, Hani; Celikel, Ece Yetkin (UNIV NIS, 2022)Let R be a commutative ring with nonzero identity.In this paper, we introduce the concept of weakly Jideals as a new generalization of Jideals. We call a proper ideal I of a ring R a weakly Jideal if whenever a, b is ... 
Weakly Jsubmodules of modules over commutative rings
Khashan, Hani A.; Celikel, Ece Yetkin (WORLD SCIENTIFIC PUBL CO PTE LTD, JUL 2023)Let R be a commutative ring with identity and M be a unitary Rmodule. By J(R), we denote the Jacobson radical of R. The purpose of this paper is to introduce the concept of weakly Jsubmodules generalizing Jsubmodules. ...