In this paper, we will introduce the notion of quasi 2-absorbing second modules over a commutative ring and obtain some basic properties of this class of modules.
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 submodules (II), Mediterr. J. Math. 9 (2) (2012), 329-338.
Ansari-Toroghy, H. and Farshadifar, F., The Zariski topology on the second spectrum of a module, Algebra Colloq. 21 (04) (2014), 671-688.
Ansari-Toroghy, H. and F. Farshadifar, 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, to appear.
Badawi, A., On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. 75 (2007), 417-429.
Badawi, A., Tekir, U. and Yetkin, E., On 2-absorbing primary ideals in commutative rings. Bull. Korean Math. Soc. 51 (4) (2014), 1163?1173.
Barnard, A., Multiplication modules, J. Algebra 71 (1981), 174-178.
Ceken, S., Alkan, M. and Smith, P.F., Second modules over noncommutative rings, Comm. Algebra, 41(1) (2013), 83-98.
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 Pure Appl. Math. 249 (2006), 121--145.
Payrovi, Sh. and Babaei, S., On the 2-absorbing ideals, Int. Math. Forum 7 (2012), 265-271.
Payrovi, Sh. and Babaei, S., On 2-absorbing submodules, Algebra Collq., 19 (2012), 913-920.
Sharp, R. Y., Step in Commutative Algebra, Cambridge University Press, 1990.
Tekir, U., Koc, S. Oral, K.H. and Shum, K.P., On 2-absorbing quasi-primary ideals in commutative rings, Communications in Mathematics and Statistics, 4 (1) (2016), 55-62 .
Yassemi, S., The dual notion of prime submodules, Arch. Math. (Brno) 37 (2001), 273--278.
Year 2019,
Volume: 68 Issue: 1, 1090 - 1096, 01.02.2019
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 submodules (II), Mediterr. J. Math. 9 (2) (2012), 329-338.
Ansari-Toroghy, H. and Farshadifar, F., The Zariski topology on the second spectrum of a module, Algebra Colloq. 21 (04) (2014), 671-688.
Ansari-Toroghy, H. and F. Farshadifar, 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, to appear.
Badawi, A., On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. 75 (2007), 417-429.
Badawi, A., Tekir, U. and Yetkin, E., On 2-absorbing primary ideals in commutative rings. Bull. Korean Math. Soc. 51 (4) (2014), 1163?1173.
Barnard, A., Multiplication modules, J. Algebra 71 (1981), 174-178.
Ceken, S., Alkan, M. and Smith, P.F., Second modules over noncommutative rings, Comm. Algebra, 41(1) (2013), 83-98.
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 Pure Appl. Math. 249 (2006), 121--145.
Payrovi, Sh. and Babaei, S., On the 2-absorbing ideals, Int. Math. Forum 7 (2012), 265-271.
Payrovi, Sh. and Babaei, S., On 2-absorbing submodules, Algebra Collq., 19 (2012), 913-920.
Sharp, R. Y., Step in Commutative Algebra, Cambridge University Press, 1990.
Tekir, U., Koc, S. Oral, K.H. and Shum, K.P., On 2-absorbing quasi-primary ideals in commutative rings, Communications in Mathematics and Statistics, 4 (1) (2016), 55-62 .
Yassemi, S., The dual notion of prime submodules, Arch. Math. (Brno) 37 (2001), 273--278.
Ansari-toroghy, H., & Farshadifar, F. (2019). Quasi 2-absorbing second modules. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 1090-1096. https://doi.org/10.31801/cfsuasmas.508101
AMA
Ansari-toroghy H, Farshadifar F. Quasi 2-absorbing second modules. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):1090-1096. doi:10.31801/cfsuasmas.508101
Chicago
Ansari-toroghy, H., and F. Farshadifar. “Quasi 2-Absorbing Second Modules”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 1090-96. https://doi.org/10.31801/cfsuasmas.508101.
EndNote
Ansari-toroghy H, Farshadifar F (February 1, 2019) Quasi 2-absorbing second modules. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 1090–1096.
IEEE
H. Ansari-toroghy and F. Farshadifar, “Quasi 2-absorbing second modules”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 1090–1096, 2019, doi: 10.31801/cfsuasmas.508101.
ISNAD
Ansari-toroghy, H. - Farshadifar, F. “Quasi 2-Absorbing Second Modules”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 1090-1096. https://doi.org/10.31801/cfsuasmas.508101.
JAMA
Ansari-toroghy H, Farshadifar F. Quasi 2-absorbing second modules. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1090–1096.
MLA
Ansari-toroghy, H. and F. Farshadifar. “Quasi 2-Absorbing Second Modules”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 1090-6, doi:10.31801/cfsuasmas.508101.
Vancouver
Ansari-toroghy H, Farshadifar F. Quasi 2-absorbing second modules. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):1090-6.