Öz
Kaynakça
- D. D. Anderson and M. Bataineh, Generalizations of prime ideals, Comm. Algebra, 36(2) (2008), 686-696.
- D. D. Anderson and M. Winders, Idealization of a module, J. Commut. Algebra, 1(1) (2009), 3-56.
- M. F. Atiyah and I. G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, 1969.
- A. Badawi and B. Fahid, On weakly 2-absorbing $\delta$-primary ideals of commutative rings, Georgian Math. J., 27(4) (2020), 503-516.
- D. E. Dobbs, A. El Khalfi and N. Mahdou Trivial extensions satisfying certain valuation-like properties, Comm. Algebra, 47(5) (2019), 2060-2077.
- M. Ebrahimpour and R. Nekooei, On generalizations of prime ideals, Comm. Algebra, 40(4) (2012), 1268-1279.
- S. Glaz, Commutative Coherent Rings, Lecture Notes in Math., 1371, Springer-Verlag, Berlin, 1989.
- J. A. Huckaba, Commutative Rings with Zero Divisors, Monogr. Textbooks Pure Appl. Math., 117, Marcel Dekker, Inc., New York, 1988.
- R. Mohamadian, $r$-ideals in commutative rings, Turkish J. Math., 39(5) (2015), 733-749.
- U. Tekir, S. Koc and K. H. Oral, $n$-ideals of commutative rings, Filomat, 31(10) (2017), 2933-2941.
- D. Zhao, $\delta$-primary ideals of commutative rings, Kyungpook Math. J., 41(1) (2001), 17-22.
Öz
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.
Anahtar Kelimeler
Prime ideal $\delta$-primary ideal $n$-ideal $\dt$-ideal trivial ring extension
Kaynakça
- D. D. Anderson and M. Bataineh, Generalizations of prime ideals, Comm. Algebra, 36(2) (2008), 686-696.
- D. D. Anderson and M. Winders, Idealization of a module, J. Commut. Algebra, 1(1) (2009), 3-56.
- M. F. Atiyah and I. G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, 1969.
- A. Badawi and B. Fahid, On weakly 2-absorbing $\delta$-primary ideals of commutative rings, Georgian Math. J., 27(4) (2020), 503-516.
- D. E. Dobbs, A. El Khalfi and N. Mahdou Trivial extensions satisfying certain valuation-like properties, Comm. Algebra, 47(5) (2019), 2060-2077.
- M. Ebrahimpour and R. Nekooei, On generalizations of prime ideals, Comm. Algebra, 40(4) (2012), 1268-1279.
- S. Glaz, Commutative Coherent Rings, Lecture Notes in Math., 1371, Springer-Verlag, Berlin, 1989.
- J. A. Huckaba, Commutative Rings with Zero Divisors, Monogr. Textbooks Pure Appl. Math., 117, Marcel Dekker, Inc., New York, 1988.
- R. Mohamadian, $r$-ideals in commutative rings, Turkish J. Math., 39(5) (2015), 733-749.
- U. Tekir, S. Koc and K. H. Oral, $n$-ideals of commutative rings, Filomat, 31(10) (2017), 2933-2941.
- D. Zhao, $\delta$-primary ideals of commutative rings, Kyungpook Math. J., 41(1) (2001), 17-22.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Cebir ve Sayı Teorisi |
| Bölüm | Makaleler |
| Yazarlar | |
| Erken Görünüm Tarihi | 17 Şubat 2024 |
| Yayımlanma Tarihi | 12 Temmuz 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 36 Sayı: 36 |