[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2016.56.4.1085

Weakly Classical Prime Submodules

Mostafanasab, Hojjat (Department of Mathematics and Applications, University of Mohaghegh Ardabili)
Tekir, Unsal (Department of Mathematics, Marmara University)
Oral, Kursat Hakan (Department of Mathematics, Yildiz Technical University, Davutpasa Campus)

Publication Information

Kyungpook Mathematical Journal / v.56, no.4, 2016 , pp. 1085-1101 More about this Journal

Abstract

In this paper, all rings are commutative with nonzero identity. Let M be an R-module. A proper submodule N of M is called a classical prime submodule, if for each $m{\in}M$ and elements a, $b{\in}R$ , $abm{\in}N$ implies that $am{\in}N$ or $bm{\in}N$ . We introduce the concept of "weakly classical prime submodules" and we will show that this class of submodules enjoys many properties of weakly 2-absorbing ideals of commutative rings. A proper submodule N of M is a weakly classical prime submodule if whenever $a,b{\in}R$ and $m{\in}M$ with $0{\neq}abm{\in}N$ , then $am{\in}N$ or $bm{\in}N$ .

Keywords

Weakly prime submodule; Classical prime submodule; Weakly classical prime submodule;

Citations & Related Records

Times Cited By KSCI : 3 (Citation Analysis)

Reference
Cited By KSCI

1	M. M. Ali, Idempotent and nilpotent submodules of multiplication modules, Comm. Algebra, 36(2008), 4620-4642. DOI
2	R. Ameri, On the prime submodules of multiplication modules, Inter. J. Math. Math. Sci., 27(2003), 1715-1724.
3	D. F. Anderson and A. Badawi, On n-absorbing ideals of commutative rings, Comm. Algebra, 39(2011), 1646-1672. DOI
4	D. D. Anderson and E. Smith, Weakly prime ideals, Houston J. Math., 29(2003), 831-840.
5	A. Azizi, On prime and weakly prime submodules, Vietnam J. Math., 36(3)(2008), 315-325.
6	A. Azizi, Weakly prime submodules and prime submodules, Glasgow Math. J., 48(2006), 343-346. DOI
7	A. Badawi, On 2-absorbing ideals of commutative rings, Bull.Austral. Math. Soc., 75(2007), 417-429. DOI
8	A. Badawi and A. Y. Darani, On weakly 2-absorbing ideals of commutative rings, Houston J. Math., 39(2)(2013), 441-452.
9	A. Badawi, U. Tekir, E. A. Ugurlu, G. Ulucak and E. Y. Celikel, Generalizations of 2-absorbing primary ideals of commutative rings, Turkish J. Math., 40(2016), 703-717. DOI
10	A. Badawi, U. Tekir and E. Yetkin, On 2-absorbing primary ideals of commutative rings, Bull. Korean Math. Soc., 51(4)(2014), 1163-1173. DOI
11	M. Behboodi and H. Koohy, Weakly prime modules, Vietnam J. Math., 32(2)(2004), 185-195.
12	A. Badawi, U. Tekir and E. Yetkin, On weakly 2-absorbing primary ideals of commutative rings, J. Korean Math. Soc., 52(1)(2015), 97-111. DOI
13	M. Behboodi, A generalization of Bears lower nilradical for modules, J. Algebra Appl., 6(2)(2007), 337-353. DOI
14	M. Behboodi, On weakly prime radical of modules and semi-compatible modules, Acta Math. Hungar., 113(3)(2006), 239-250.
15	M. Behboodi and S. H. Shojaee, On chains of classical prime submodules and dimen-sion theory of modules, Bull. Iranian Math. Soc., 36(1)(2010), 149-166.
16	J. Dauns, Prime modules, J. Reine Angew. Math., 298(1978), 156-181.
17	S. Ebrahimi Atani and F. Farzalipour, On weakly prime submodules, Tamk. J. Math., 38(3)(2007), 247-252.
18	Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16(1988), 755-779. DOI
19	C.-P. Lu, Prime submodules of modules, Comm. Math. Univ. Sancti Pauli, 33(1984), 61-69.
20	R. L. McCasland and M. E. Moore, Prime submodules, Comm. Algebra, 20(1992), 1803-1817. DOI
21	H. Mostafanasab and A. Y. Darani, On $\phi$ -n-absorbing primary ideals of commutative rings, J. Korean Math. Soc., 53(3)(2016), 549-582. DOI
22	P. Quartararo and H. S. Butts, Finite unions of ideals and modules, Proc. Amer. Math. Soc., 52(1975), 91-96. DOI
23	R.Y. Sharp, Steps in commutative algebra, Second edition, Cambridge University Press, Cambridge, 2000.
24	P. F. Smith, Some remarks on multiplication modules, Arch. Math., 50(1988), 223-235. DOI
25	A. Yousean Darani and F. Soheilnia, On 2-absorbing and weakly 2-absorbing submodules, Thai J. Math., 9(2011), 577-584.