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J-IDEALS OF COMMUTATIVE RINGS

Yıl 2021, Cilt: 29 Sayı: 29, 148 - 164, 05.01.2021
https://doi.org/10.24330/ieja.852139

Öz

Let $R$ be a commutative ring with identity and $N(R)$ and
$J\left(R\right)$ denote the nilradical and the Jacobson radical
of $R$, respectively. A proper ideal $I$ of $R$ is called an
n-ideal if for every $a,b\in R$, whenever $ab\in I$\ and $a\notin
N(R)$, then $b\in I$. In this paper, we introduce and study
J-ideals as a new generalization of n-ideals in commutative rings.
A proper ideal $I$\ of $R$\ is called a J-ideal if whenever $ab\in
I$\ with $a\notin J\left(R\right) $, then $b\in I$\ for every
$a,b\in R$. We study many properties and examples of such class of
ideals. Moreover, we investigate its relation with some other
classes of ideals such as r-ideals, prime, primary and maximal
ideals. Finally, we, more generally, define and study J-submodules
of an $R$-modules $M$. We clarify some of their properties
especially in the case of multiplication modules.

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.
  • D. D. Anderson, T. Arabaci, U. Tekir and S. Koc, On S-multiplication modules, Comm. Algebra, 48(8) (2020), 3398-3407.
  • D. D. Anderson, M. Axtell, S. J. Forman and J. Stickles, When are associates unit multiples, Rocky Mountain J. Math., 34(3) (2004), 811-828.
  • A. Badawi, U. Tekir and E. Yetkin, On 2-absorbing primary ideals in commutative rings, Bull. Korean Math. Soc., 51(4) (2014), 1163-1173.
  • S. Ebrahimi Atani and F. Farzalipour, On weakly primary ideals, Georgian Math. J., 12(3) (2005), 423-429.
  • M. Ebrahimpour and R. Nekooei, On generalizations of prime ideals, Comm. Algebra, 40(4) (2012), 1268-1279.
  • Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16(4) (1988), 755-779.
  • H. A. Khashan, On almost prime submodules, Acta Math. Sci. Ser. B (Engl. Ed.), 32(2) (2012), 645-651.
  • R. Mohamadian, r-Ideals in commutative rings, Turkish J. Math., 39 (2015), 733-749.
  • R. Y. Sharp, Steps in Commutative Algebra, Second edition, London Mathematical Society Student Texts, 51, Cambridge University Press, Cambridge, 2000.
  • P. F. Smith, Some remarks on multiplication modules, Arch. Math. (Basel), 50(3) (1988), 223-235.
  • U. Tekir, S. Koc and K. H. Oral, n-Ideals of commutative rings, Filomat, 31(10) (2017), 2933-2941.
Yıl 2021, Cilt: 29 Sayı: 29, 148 - 164, 05.01.2021
https://doi.org/10.24330/ieja.852139

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.
  • D. D. Anderson, T. Arabaci, U. Tekir and S. Koc, On S-multiplication modules, Comm. Algebra, 48(8) (2020), 3398-3407.
  • D. D. Anderson, M. Axtell, S. J. Forman and J. Stickles, When are associates unit multiples, Rocky Mountain J. Math., 34(3) (2004), 811-828.
  • A. Badawi, U. Tekir and E. Yetkin, On 2-absorbing primary ideals in commutative rings, Bull. Korean Math. Soc., 51(4) (2014), 1163-1173.
  • S. Ebrahimi Atani and F. Farzalipour, On weakly primary ideals, Georgian Math. J., 12(3) (2005), 423-429.
  • M. Ebrahimpour and R. Nekooei, On generalizations of prime ideals, Comm. Algebra, 40(4) (2012), 1268-1279.
  • Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16(4) (1988), 755-779.
  • H. A. Khashan, On almost prime submodules, Acta Math. Sci. Ser. B (Engl. Ed.), 32(2) (2012), 645-651.
  • R. Mohamadian, r-Ideals in commutative rings, Turkish J. Math., 39 (2015), 733-749.
  • R. Y. Sharp, Steps in Commutative Algebra, Second edition, London Mathematical Society Student Texts, 51, Cambridge University Press, Cambridge, 2000.
  • P. F. Smith, Some remarks on multiplication modules, Arch. Math. (Basel), 50(3) (1988), 223-235.
  • U. Tekir, S. Koc and K. H. Oral, n-Ideals of commutative rings, Filomat, 31(10) (2017), 2933-2941.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Hani A. Khashan Bu kişi benim

Amal B. Banı-ata Bu kişi benim

Yayımlanma Tarihi 5 Ocak 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 29 Sayı: 29

Kaynak Göster

APA Khashan, H. A., & Banı-ata, A. B. (2021). J-IDEALS OF COMMUTATIVE RINGS. International Electronic Journal of Algebra, 29(29), 148-164. https://doi.org/10.24330/ieja.852139
AMA Khashan HA, Banı-ata AB. J-IDEALS OF COMMUTATIVE RINGS. IEJA. Ocak 2021;29(29):148-164. doi:10.24330/ieja.852139
Chicago Khashan, Hani A., ve Amal B. Banı-ata. “J-IDEALS OF COMMUTATIVE RINGS”. International Electronic Journal of Algebra 29, sy. 29 (Ocak 2021): 148-64. https://doi.org/10.24330/ieja.852139.
EndNote Khashan HA, Banı-ata AB (01 Ocak 2021) J-IDEALS OF COMMUTATIVE RINGS. International Electronic Journal of Algebra 29 29 148–164.
IEEE H. A. Khashan ve A. B. Banı-ata, “J-IDEALS OF COMMUTATIVE RINGS”, IEJA, c. 29, sy. 29, ss. 148–164, 2021, doi: 10.24330/ieja.852139.
ISNAD Khashan, Hani A. - Banı-ata, Amal B. “J-IDEALS OF COMMUTATIVE RINGS”. International Electronic Journal of Algebra 29/29 (Ocak 2021), 148-164. https://doi.org/10.24330/ieja.852139.
JAMA Khashan HA, Banı-ata AB. J-IDEALS OF COMMUTATIVE RINGS. IEJA. 2021;29:148–164.
MLA Khashan, Hani A. ve Amal B. Banı-ata. “J-IDEALS OF COMMUTATIVE RINGS”. International Electronic Journal of Algebra, c. 29, sy. 29, 2021, ss. 148-64, doi:10.24330/ieja.852139.
Vancouver Khashan HA, Banı-ata AB. J-IDEALS OF COMMUTATIVE RINGS. IEJA. 2021;29(29):148-64.

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