Browsing by Author "Çelikel, Ece Yetkin"

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Clear graph of a ring

Mir, Shabir Ahmad; Abdioğlu, Cihat; Rehman, Nadeem ur; Nazim, Mohd; Akkafa, Muhammed; Çelikel, Ece Yetkin (Indian National Science Academy, 2024)

This research article introduces the concept of the clear graph associated with a ring R with identity, denoted as Cr(R). This graph comprises vertices of the form {(x,u):x is a unit regular element of R and u is a unit ...
Generalizations of 1-absorbing primary ideals of commutative rings

Çelikel, Ece Yetkin (Politechnica University of Bucharest, 2020)

Let R be a commutative ring with identity. In this paper, we extend the concept of 1-absorbing primary ideals to the concept of ֆ-1-absorbing primary ideals. Let ֆ: S(R) → S(R) ∪ {∅} be a function, where S(R) is the set ...
On 1-absorbing primary ideals of commutative rings

Badawi, Ayman; Çelikel, Ece Yetkin (World Scientific Publishing Co. Pte Ltd, 2019)

Let R be a commutative ring with nonzero identity. In this paper, we introduce the concept of 1-absorbing primary ideals in commutative rings. A proper ideal I of R is called a 1-absorbing primary ideal of R if whenever ...
(δ, 2)-Primary Ideals of a Commutative Ring

Ulucak, Gülşen; Çelikel, Ece Yetkin (Springer Science and Business Media Deutschland GmbH, December 2)

Let R be a commutative ring with nonzero identity, let I(R) be the set of all ideals of R and δ: I(R) → I(R) an expansion of ideals of R defined by I ↦ δ(I). We introduce the concept of (δ, 2)-primary ideals in commutative ...