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(n − 1, n)-weakly prime submodules in direct product of modules | ||
| Journal of Hyperstructures | ||
| دوره 6، شماره 1، شهریور 2017، صفحه 10-16 اصل مقاله (272.85 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2017.2657 | ||
| نویسنده | ||
| M. Ebrahimpour* | ||
| Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O.Box 518, Rafsanjan, Iran | ||
| چکیده | ||
| Let n ≥ 2 be a positive integer, R be a commutative ring with identity and M be a unitary R-module . In this paper we study the (n − 1, n)-weakly prime submodules of direct product of modules. Also, we show that for some special cases, every proper submodule is (n − 1, n)-weakly prime. | ||
| کلیدواژه‌ها | ||
| Prime submodule؛ Weakly prime submodule؛ Quasi-local ring؛ (n − 1؛ n)-weakly prime submodule | ||
| مراجع | ||
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[1] M. Ebrahimpour and R. Nekooei, On generalizations of prime ideals, Commun. Algebra, 40 (2012), 1268–1279. [2] M. Ebrahimpour and R. Nekooei, On generalizations of prime submodules, Bull. Iran. Math. Soc., 39(5) (2013), 919–939. [3] M. Ebrahimpour, On generalisations of almost prime and weakly pime ideals, Bull. Iran. Math. Soc., 40(2) (2014), 531–540. [4] M. Ebrahimpour, Some remarks on generalizations of multiplicatively-closed sub-sets, J. Alg. Systems, 4(1) (2016), 15–27. [5] M. Ebrahimpour, Some generalizations of weakly prime submodules, to appear in Transactions on Algebra and its Applications. [6] S. Galovich, Unique factorization rings with zero divisors, Math. Mag., 51 (1978), 276–283. [7] C. P. Lu, Prime submodules, Comm. Math. Univ. Sancti Pauli, 33 (1984), 61–69. [8] R. L. Mc Casland and M. E. Moore, Prime submodules, Commun. Algebra, 20 (1992), 1803–1817. [9] R. L. Mc Casland and P. F. Smith,Prime submodules of Noetherian modules,Rocky Mountain J.Math.,23(1993),1041–1062. [10] M. E. Moore and S. J. Smith, Prime and radical submodules of modules over commutative rings, Commun. Algebra, 30 (2010), 5037–5064. [11] R. Moradi and M. Ebrahimpour, On φ-2-Absorbing primary submodules, to ap-pear in Acta Math. Vietnam. [12] R. Nekooei, Weakly prime submodules, FJMS. , 39(2) (2010), 185–192. [13] R.Y. Sharp, Steps in commutative algebra, Cambridge: Cambridge University Prees (2000). [14] N. Zamani, φ-prime submodules, Glasgow Math. J. Trust (2009), 1–7. | ||
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