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Classical and strongly classical 2-absorbing second submodules

Yıl 2020, Cilt: 69 Sayı: 1, 123 - 136, 30.06.2020
https://doi.org/10.31801/cfsuasmas.550201

Öz

‎In this paper‎, ‎we will introduce the concept of classical (resp‎. ‎strongly classical) 2-absorbing second submodules of modules over a commutative ring as a generalization of 2-absorbing (resp‎. ‎strongly 2-absorbing) second submodules and investigate some basic properties of these classes of modules‎.

Kaynakça

  • Ansari-Toroghy, H. and Farshadifar, F., The dual notion of some generalizations of prime submodules, Comm. Algebra, 39 (2011), 2396-2416.
  • Ansari-Toroghy, H. and Farshadifar, F., The dual notion of multiplication modules, Taiwanese J. Math. 11 (4) (2007), 1189--1201.
  • Ansari-Toroghy, H. and Farshadifar, F., On the dual notion of prime submodules, Algebra Colloq. 19 (Spec 1)(2012), 1109-1116.
  • Ansari-Toroghy, H. and Farshadifar, F., On the dual notion of prime radicals of submodules, Asian Eur. J. Math. 6 (2) (2013), 1350024 (11 pages).
  • Ansari-Toroghy, H. and Farshadifar, F., Some generalizations of second submodules, Palestine Journal of Mathematics, 8(2) (2019), 1-10.
  • Ansari-Toroghy, H., Farshadifar, F., and Pourmortazavi, S. S., On the P-interiors of submodules of Artinian modules, Hacettepe Journal of Mathematics and Statistics, 45(3) (2016), 675-682.
  • Badawi, A., On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. 75 (2007), 417-429.
  • Barnard, A., Multiplication modules, J. Algebra, 71 (1981), 174-178.
  • Ceken, S., Alkan, M. and Smith, P.F., The dual notion of the prime radical of a module, J. Algebra, 392 (2013), 265-275.
  • Darani, A. Y. and Soheilnia, F., 2-absorbing and weakly 2-absorbing submoduels, Thai J. Math. 9(3) (2011), 577-584.
  • Dauns, J ., Prime submodules, J. Reine Angew. Math., 298 (1978), 156--181.
  • Fuchs, L., Heinzer, W. and Olberding, B., Commutative ideal theory without finiteness conditions: Irreducibility in the quotient filed, in : Abelian Groups, Rings, Modules, and Homological Algebra, Lect. Notes in Pure Appl. Math. 249 (2006), 121--145.
  • Kaplansky, I., Commutative rings, University of Chicago Press, 1978.
  • Mostafanasab, H., Tekir, U. and Oral, K.H., Classical 2-absorbing submodules of modules over commutative rings, European Journal of Pure and Applied Mathematics, 8(3) (2015), 417-430.
  • Payrovi, Sh. and Babaei, S., On 2-absorbing submodules, Algebra Collq. 19 (2012), 913-920.
  • Quartararo, P. and Butts, H. S., Finite unions of ideals and modules, Proc. Amer. Math. Soc. 52 (1975), 91-96.
  • Sharpe, D.W. and Vamos, P., Injective modules, Cambridge University Press, 1972.
  • Yassemi, S., The dual notion of prime submodules, Arch. Math. (Brno) 37 (2001), 273--278.
  • Yassemi, S., The dual notion of the cyclic modules, Kobe. J. Math. 15 (1998), 41--46.
Yıl 2020, Cilt: 69 Sayı: 1, 123 - 136, 30.06.2020
https://doi.org/10.31801/cfsuasmas.550201

Öz

Kaynakça

  • Ansari-Toroghy, H. and Farshadifar, F., The dual notion of some generalizations of prime submodules, Comm. Algebra, 39 (2011), 2396-2416.
  • Ansari-Toroghy, H. and Farshadifar, F., The dual notion of multiplication modules, Taiwanese J. Math. 11 (4) (2007), 1189--1201.
  • Ansari-Toroghy, H. and Farshadifar, F., On the dual notion of prime submodules, Algebra Colloq. 19 (Spec 1)(2012), 1109-1116.
  • Ansari-Toroghy, H. and Farshadifar, F., On the dual notion of prime radicals of submodules, Asian Eur. J. Math. 6 (2) (2013), 1350024 (11 pages).
  • Ansari-Toroghy, H. and Farshadifar, F., Some generalizations of second submodules, Palestine Journal of Mathematics, 8(2) (2019), 1-10.
  • Ansari-Toroghy, H., Farshadifar, F., and Pourmortazavi, S. S., On the P-interiors of submodules of Artinian modules, Hacettepe Journal of Mathematics and Statistics, 45(3) (2016), 675-682.
  • Badawi, A., On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. 75 (2007), 417-429.
  • Barnard, A., Multiplication modules, J. Algebra, 71 (1981), 174-178.
  • Ceken, S., Alkan, M. and Smith, P.F., The dual notion of the prime radical of a module, J. Algebra, 392 (2013), 265-275.
  • Darani, A. Y. and Soheilnia, F., 2-absorbing and weakly 2-absorbing submoduels, Thai J. Math. 9(3) (2011), 577-584.
  • Dauns, J ., Prime submodules, J. Reine Angew. Math., 298 (1978), 156--181.
  • Fuchs, L., Heinzer, W. and Olberding, B., Commutative ideal theory without finiteness conditions: Irreducibility in the quotient filed, in : Abelian Groups, Rings, Modules, and Homological Algebra, Lect. Notes in Pure Appl. Math. 249 (2006), 121--145.
  • Kaplansky, I., Commutative rings, University of Chicago Press, 1978.
  • Mostafanasab, H., Tekir, U. and Oral, K.H., Classical 2-absorbing submodules of modules over commutative rings, European Journal of Pure and Applied Mathematics, 8(3) (2015), 417-430.
  • Payrovi, Sh. and Babaei, S., On 2-absorbing submodules, Algebra Collq. 19 (2012), 913-920.
  • Quartararo, P. and Butts, H. S., Finite unions of ideals and modules, Proc. Amer. Math. Soc. 52 (1975), 91-96.
  • Sharpe, D.W. and Vamos, P., Injective modules, Cambridge University Press, 1972.
  • Yassemi, S., The dual notion of prime submodules, Arch. Math. (Brno) 37 (2001), 273--278.
  • Yassemi, S., The dual notion of the cyclic modules, Kobe. J. Math. 15 (1998), 41--46.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Faranak Farshadifar 0000-0001-7600-994X

Habibollah Ansari-toroghy Bu kişi benim 0000-0001-7310-0924

Yayımlanma Tarihi 30 Haziran 2020
Gönderilme Tarihi 6 Nisan 2019
Kabul Tarihi 3 Eylül 2019
Yayımlandığı Sayı Yıl 2020 Cilt: 69 Sayı: 1

Kaynak Göster

APA Farshadifar, F., & Ansari-toroghy, H. (2020). Classical and strongly classical 2-absorbing second submodules. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 123-136. https://doi.org/10.31801/cfsuasmas.550201
AMA Farshadifar F, Ansari-toroghy H. Classical and strongly classical 2-absorbing second submodules. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Haziran 2020;69(1):123-136. doi:10.31801/cfsuasmas.550201
Chicago Farshadifar, Faranak, ve Habibollah Ansari-toroghy. “Classical and Strongly Classical 2-Absorbing Second Submodules”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, sy. 1 (Haziran 2020): 123-36. https://doi.org/10.31801/cfsuasmas.550201.
EndNote Farshadifar F, Ansari-toroghy H (01 Haziran 2020) Classical and strongly classical 2-absorbing second submodules. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 123–136.
IEEE F. Farshadifar ve H. Ansari-toroghy, “Classical and strongly classical 2-absorbing second submodules”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 69, sy. 1, ss. 123–136, 2020, doi: 10.31801/cfsuasmas.550201.
ISNAD Farshadifar, Faranak - Ansari-toroghy, Habibollah. “Classical and Strongly Classical 2-Absorbing Second Submodules”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (Haziran 2020), 123-136. https://doi.org/10.31801/cfsuasmas.550201.
JAMA Farshadifar F, Ansari-toroghy H. Classical and strongly classical 2-absorbing second submodules. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:123–136.
MLA Farshadifar, Faranak ve Habibollah Ansari-toroghy. “Classical and Strongly Classical 2-Absorbing Second Submodules”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 69, sy. 1, 2020, ss. 123-36, doi:10.31801/cfsuasmas.550201.
Vancouver Farshadifar F, Ansari-toroghy H. Classical and strongly classical 2-absorbing second submodules. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):123-36.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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