zbMATH — the first resource for mathematics

A generalization of graded prime submodules over non-commutative graded rings. (English) Zbl 1443.16048
Summary: Let \(G\) be a group with identity \(e\). Let \(R\) be an associative \(G\)-graded ring and \(M\) be a \(G\)-graded \(R\)-module. In this article, we intruduce the concept of graded 2-absorbing submodules as a generalization of graded prime submodules over non-commutative graded rings. Moreover, we get some properties of such graded submodules.
16W50 Graded rings and modules (associative rings and algebras)
13A02 Graded rings
Full Text: DOI
[1] R. Abu-Dawwas, M. Bataineh and M. Al-Muanger,Graded prime submodules over non-commutative rings, Vietnam J. Math., (3)46(2018), 681-692. · Zbl 1393.16035
[2] K. Al-Zobi, R. Abu-Dawwas and S. Ceken,On graded2-absorbing and graded weakly2-absorbing ideals, Hacet. J. Math. Stat., (4)48(2019), 724-731.
[3] A. Badawi,On2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc., (3)75(2007), 417-429. · Zbl 1120.13004
[4] S. Ebrahimi Atani,On graded prime submodules, Chiang Mai J. Sci., (1)33 (2006), 3-7. · Zbl 1099.13001
[5] S. Ebrahimi Atani and F. Farzalipour,On graded secondary modules, Turk. J. Math.,31(2007), 371-378. · Zbl 1132.13001
[6] F. Farzalipour and P. Ghiasvand,On the union of graded prime submodules, Thai. J. of Math., (1)9(2011), 49-55. · Zbl 1260.13001
[7] P. Ghiasvand and F. Farzalipour,On graded weak multiplication modules, Tamkang J. of Math., (2)43(2012), 171-177. · Zbl 1254.13013
[8] P. Ghiasvand and F. Farzalipour,On the graded primary radical of graded submodules, Advances and Applications in Math. Sci., (1)10(2011), 1-7. · Zbl 1245.13002
[9] N. J. Groenewald and Bac T. Nguyen,On2-absorbing modules over noncommutative rings, International Electronic Journal of Algebra,25(2019), 212- 223. · Zbl 1406.16001
[10] N. Nastasescu and F. Van Oystaeyen,Graded Rings Theory, Mathematical Library 28, North Holand, Amsterdam, 1937. · Zbl 1043.16017
[11] N. Nastasescu and F. Van Oystaeyen,Methods of Graded Rings, Lecture Notes in Mathematics, vol. 1836, Springer, Berlin 2004. · Zbl 1043.16017
[12] Sh. Payrovi and S. Babaei,On2-absorbing submodules, Algebra Collq.,19 (2012), 913-920. · Zbl 1294.13015
[13] M. Refaei and K. Al-Zobi,On graded primary ideals, Turk. J. Math., (3)28 (2004), 217-229.
[14] R. N. Uregen, U. Tekir, K. P. Shum and S. Koc,On graded2-absorbing quasi primary ideals, Southeast Asian Bulletin of Math.,43(2019), 601-613. · Zbl 1449.13004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.