$\\delta (0)$-Ideals of Commutative Rings

Authors : Mohamed Chhiti, Bayram Ali Ersoy, Khalid Kaıba, Ünsal Tekir

Pages : 16-28

Doi:10.24330/ieja.1438744

View : 102 | Download : 104

Publication Date : 2024-07-12

Article Type : Research Paper

Abstract :Let $R$ be a commutative ring with nonzero identity, let $\\I (R)$ be the set of all ideals of $R$ and $\\delta : \\I (R)\\rightarrow\\I (R) $ be a function. Then $\\delta$ is called an expansion function of ideals of $R$ if whenever $L, I, J$ are ideals of $R$ with $J \\subseteq I$, we have $L \\subseteq\\delta(L)$ and $\\delta(J)\\subseteq\\delta(I)$. In this paper, we present the concept of $\\dt$-ideals in commutative rings. A proper ideal $I$ of $R$ is called a $\\dt$-ideal if whenever $a$, $b$ $\\in R$ with $ab\\in I$ and $a\\notin \\delta (0)$, we have $b\\in I$. Our purpose is to extend the concept of $n$-ideals to $\\dt$-ideals of commutative rings. Then we investigate the basic properties of $\\dt$-ideals and also, we give many examples about $\\dt$-ideals.
Keywords : Prime ideal, \\delta primary ideal, n ideal, \\dt ideal, trivial ring extension