Araştırma Çıktıları

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Browsing Araştırma Çıktıları by Subject "(2, n)-ideal"

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    (2, J)-IDEALS IN COMMUTATIVE RINGS
    (PUBL HOUSE BULGARIAN ACAD SCI, 2020) Yildiz, Eda; Tekir, Unsal; Koc, Suat
    Let A be a commutative ring with nonzero identity. In this paper, we introduce the concept of (2, J)-ideal as a generalization of J-ideal. A proper ideal P of A is said to be a (2, J)-ideal if whenever abc is an element of P and a, b, c is an element of A, then ab is an element of P or ac is an element of Jac(A) or be is an element of Jac(A). Various examples and characterizations of (2, J)-ideals are given. Also, we study many properties of (2, J)-ideals and use them to characterize certain classes of rings such as quasi-local rings and Artinian rings.
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    On quası n-ideals of commutative rings
    (2022-12-01) ASLANKARAYİĞİT UĞURLU, EMEL; Anebri A., Mahdou N., ASLANKARAYİĞİT UĞURLU E.
    Let R be a commutative ring with a nonzero identity. In this study, we present a new class of ideals lying properly between the class of n-ideals and the class of (2, n)-ideals. A proper ideal I of R is said to be a quasi n-ideal if root I is an n-ideal of R. Many examples and results are given to disclose the relations between this new concept and others that already exist, namely, the n-ideals, the quasi primary ideals, the (2, n)-ideals and the pr-ideals. Moreover, we use the quasi n-ideals to characterize some kind of rings. Finally, we investigate quasi n-ideals under various contexts of constructions such as direct product, power series, idealization, and amalgamation of a ring along an ideal.