Affiliation:
1. University S.M. Ben Abdellah
2. YILDIZ TEKNİK ÜNİVERSİTESİ
3. MARMARA UNIVERSITY
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.
Publisher
The International Electronic Journal of Algebra
Reference11 articles.
1. D. D. Anderson and M. Bataineh, Generalizations of prime ideals, Comm. Algebra, 36(2) (2008), 686-696.
2. D. D. Anderson and M. Winders, Idealization of a module, J. Commut. Algebra, 1(1) (2009), 3-56.
3. M. F. Atiyah and I. G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, 1969.
4. A. Badawi and B. Fahid, On weakly 2-absorbing $\delta$-primary ideals of commutative rings, Georgian Math. J., 27(4) (2020), 503-516.
5. D. E. Dobbs, A. El Khalfi and N. Mahdou Trivial extensions satisfying certain valuation-like properties, Comm. Algebra, 47(5) (2019), 2060-2077.