Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2022, Cilt: 5 Sayı: 4, 199 - 208, 30.12.2022
https://doi.org/10.33434/cams.1195074

Öz

Kaynakça

  • [1] D. D. Anderson, Some remarks on multiplication ideals, Math. Japon, 25 (1980), 463-469.
  • [2] D. D. Anderson, E. Smith, Weakly prime ideals, Houston J. Math., 229 (4), 831-840.
  • [3] R. E. Atani, The ideal theory in quotients of commutative semirings, Glas. Math., 42 (2007), 301-308.
  • [4] S. E. Atani, R. E. Atani, Ideal theory in commutative semirings, Bu. Acad. Stiinte Repub. Mold. Mat., 2 (2009), 14-23.
  • [5] S. E. Atani, R. E. Atani, Some remarks on partitioning semirings, An. St. Univ. Ovidius Constants, 18 (2010), 49-62.
  • [6] M. F. Atiyah, I. G. Mac Donalel, An Intoduction to Commutative Algebra, Addison-Wesley Publishing Company, 1969.
  • [7] A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Aust. Math. Soc., 75(3) (2007), 417-429.
  • [8] A. Badawi, E. Y. Celikel, On weakly 1-absorbing primary ideals of commutative rings, Algebra Colloq., 29(2), 189-202.
  • [9] A. Badawi, E. Y. Celikel, On 1-absorbing primary ideals of a commutative ring, J. Algebra Its Appl., 19(6), 050111.
  • [10] S. Darani, On 2-absorbing and weakly 2-absorbing ideals of commutative semirings, Kyungpook Math. J., 52 (2012), 91-97.
  • [11] J. N. Ghaudhari, V. Gupta, Prime ideals in semirings, Bull. Malaysian Math. Sci. Soc., 34 (2011), 415-421.
  • [12] J. N. Ghaudhari, 2-absorbing ideals in semirings, Int. J. Algebra, 6 (2012), 265-270.
  • [13] J. S. Golan, Semirings and Their Applications, Kluwer Acadimic Publisher’s, Dordrecht, 1999.
  • [14] M. Henricksen, Ideals in semirings with commutative addition, American Mathematics Society, 6 (1958), 3-12.
  • [15] P. Kumar. M. K. Dubey, P. Sarohe, On 2-absorbing primary ideals in commutative semirings, Eur. J. Pure Appl. Math., 9 (2016), 186-195.
  • [16] P. Nasehpour, Some remarks on semirings and their ideals, Asian-Eur. J. Math., 12(7), 2050002.
  • [17] R. J. Nezhad, A note on divided ideals, Pure Math. A, 22, 61-64.
  • [18] L. Sawalmeh, M. Saleh, On 2-absorbing ideals of commutative semirings, J. Algebra Its Appl., To appear.
  • [19] D. A. Smith, On semigroups, semirings and rings of quotients, J. Sci. Hirshimo Univ. Ser. Math., 2 (1966), 123-130.
  • [20] H. S. Vandiver, Note on a simple of algebra in which the cancellation law of addition dose not hold, Bull. Amer. Math. Soc., 40, 914-920.
  • [21] O. Zariski, P. Samuel, Commutative Algebra, V.I. Princeton, 1958.

On Weakly 1-Absorbing Primary Ideals of Commutative Semirings

Yıl 2022, Cilt: 5 Sayı: 4, 199 - 208, 30.12.2022
https://doi.org/10.33434/cams.1195074

Öz

Let $R$ be a commutative semiring with $ 1 \neq0$. In this paper, we study the concept of weakly 1-absorbing primary ideal which is a generalization of 1-absorbing ideal over commutative semirings . A proper ideal $I$ of a semiring $R$ is called a weakly 1-absorbing primary ideal if whenever nonunit elements $a,b,c \in R$ and $0 \neq abc \in I$, then $ab \in I $, or $c \in \sqrt{I}$. A number of results concerning weakly 1-absorbing primary ideals and examples of weakly 1-absorbing primary ideals are given. An ideal is called a subtractive ideal $I$ of a semiring $R$ is an ideal such that if $ x,x+y\in I$, then $ y\in I$. Subtractive ideals or k-ideals are helpful in proving in many results related to ideal theory over semirings.

Kaynakça

  • [1] D. D. Anderson, Some remarks on multiplication ideals, Math. Japon, 25 (1980), 463-469.
  • [2] D. D. Anderson, E. Smith, Weakly prime ideals, Houston J. Math., 229 (4), 831-840.
  • [3] R. E. Atani, The ideal theory in quotients of commutative semirings, Glas. Math., 42 (2007), 301-308.
  • [4] S. E. Atani, R. E. Atani, Ideal theory in commutative semirings, Bu. Acad. Stiinte Repub. Mold. Mat., 2 (2009), 14-23.
  • [5] S. E. Atani, R. E. Atani, Some remarks on partitioning semirings, An. St. Univ. Ovidius Constants, 18 (2010), 49-62.
  • [6] M. F. Atiyah, I. G. Mac Donalel, An Intoduction to Commutative Algebra, Addison-Wesley Publishing Company, 1969.
  • [7] A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Aust. Math. Soc., 75(3) (2007), 417-429.
  • [8] A. Badawi, E. Y. Celikel, On weakly 1-absorbing primary ideals of commutative rings, Algebra Colloq., 29(2), 189-202.
  • [9] A. Badawi, E. Y. Celikel, On 1-absorbing primary ideals of a commutative ring, J. Algebra Its Appl., 19(6), 050111.
  • [10] S. Darani, On 2-absorbing and weakly 2-absorbing ideals of commutative semirings, Kyungpook Math. J., 52 (2012), 91-97.
  • [11] J. N. Ghaudhari, V. Gupta, Prime ideals in semirings, Bull. Malaysian Math. Sci. Soc., 34 (2011), 415-421.
  • [12] J. N. Ghaudhari, 2-absorbing ideals in semirings, Int. J. Algebra, 6 (2012), 265-270.
  • [13] J. S. Golan, Semirings and Their Applications, Kluwer Acadimic Publisher’s, Dordrecht, 1999.
  • [14] M. Henricksen, Ideals in semirings with commutative addition, American Mathematics Society, 6 (1958), 3-12.
  • [15] P. Kumar. M. K. Dubey, P. Sarohe, On 2-absorbing primary ideals in commutative semirings, Eur. J. Pure Appl. Math., 9 (2016), 186-195.
  • [16] P. Nasehpour, Some remarks on semirings and their ideals, Asian-Eur. J. Math., 12(7), 2050002.
  • [17] R. J. Nezhad, A note on divided ideals, Pure Math. A, 22, 61-64.
  • [18] L. Sawalmeh, M. Saleh, On 2-absorbing ideals of commutative semirings, J. Algebra Its Appl., To appear.
  • [19] D. A. Smith, On semigroups, semirings and rings of quotients, J. Sci. Hirshimo Univ. Ser. Math., 2 (1966), 123-130.
  • [20] H. S. Vandiver, Note on a simple of algebra in which the cancellation law of addition dose not hold, Bull. Amer. Math. Soc., 40, 914-920.
  • [21] O. Zariski, P. Samuel, Commutative Algebra, V.I. Princeton, 1958.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Mohammad Saleh 0000-0002-4254-2540

Ibaa Muraa Bu kişi benim

Yayımlanma Tarihi 30 Aralık 2022
Gönderilme Tarihi 26 Ekim 2022
Kabul Tarihi 29 Aralık 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 4

Kaynak Göster

APA Saleh, M., & Muraa, I. (2022). On Weakly 1-Absorbing Primary Ideals of Commutative Semirings. Communications in Advanced Mathematical Sciences, 5(4), 199-208. https://doi.org/10.33434/cams.1195074
AMA Saleh M, Muraa I. On Weakly 1-Absorbing Primary Ideals of Commutative Semirings. Communications in Advanced Mathematical Sciences. Aralık 2022;5(4):199-208. doi:10.33434/cams.1195074
Chicago Saleh, Mohammad, ve Ibaa Muraa. “On Weakly 1-Absorbing Primary Ideals of Commutative Semirings”. Communications in Advanced Mathematical Sciences 5, sy. 4 (Aralık 2022): 199-208. https://doi.org/10.33434/cams.1195074.
EndNote Saleh M, Muraa I (01 Aralık 2022) On Weakly 1-Absorbing Primary Ideals of Commutative Semirings. Communications in Advanced Mathematical Sciences 5 4 199–208.
IEEE M. Saleh ve I. Muraa, “On Weakly 1-Absorbing Primary Ideals of Commutative Semirings”, Communications in Advanced Mathematical Sciences, c. 5, sy. 4, ss. 199–208, 2022, doi: 10.33434/cams.1195074.
ISNAD Saleh, Mohammad - Muraa, Ibaa. “On Weakly 1-Absorbing Primary Ideals of Commutative Semirings”. Communications in Advanced Mathematical Sciences 5/4 (Aralık 2022), 199-208. https://doi.org/10.33434/cams.1195074.
JAMA Saleh M, Muraa I. On Weakly 1-Absorbing Primary Ideals of Commutative Semirings. Communications in Advanced Mathematical Sciences. 2022;5:199–208.
MLA Saleh, Mohammad ve Ibaa Muraa. “On Weakly 1-Absorbing Primary Ideals of Commutative Semirings”. Communications in Advanced Mathematical Sciences, c. 5, sy. 4, 2022, ss. 199-08, doi:10.33434/cams.1195074.
Vancouver Saleh M, Muraa I. On Weakly 1-Absorbing Primary Ideals of Commutative Semirings. Communications in Advanced Mathematical Sciences. 2022;5(4):199-208.

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