On graded quasi-primary submodules of graded modules over graded commutative rings

Khaldoun falah Al-Zoubi; Rweili Alkhalaf

doi:10.5269/bspm.41917

Khaldoun falah Al-Zoubi Jordan University of Science and Technology http://orcid.org/0000-0001-6082-4480
Rweili Alkhalaf Jordan University ofScience and Technology

DOI: https://doi.org/10.5269/bspm.41917

Abstract

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we introduce the concept of graded quasi-primary submodules of graded modules over graded commutative rings. Various properties of graded quasi-primary submodules are considered.

Downloads

Download data is not yet available.

Author Biographies

Khaldoun falah Al-Zoubi, Jordan University of Science and Technology

Department of Mathematics and Statistics

Rweili Alkhalaf, Jordan University ofScience and Technology

Department of Mathematics and Statistics

References

Al-Zoubi, K., The graded primary radical of a graded submodules, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.), 1, 395-402, ( 2016).

Al-Zoubi, K., Abu-Dawwas, R. and Al-Ayyoub, I., Graded semiprime submodules and graded semi-radical of graded submodules in graded modules, Ricerche mat., 66(2), 449-455, (2017).

Al-Zoubi, K. and Al-Dolat, M., On graded classical primary submodules, Adv. Pure Appl. Math., 7 (2), 93-96, ( 2016).

Al-Zoubi, K. and Al-Dolat, M., On graded primary-like submodules of graded modules over graded commutative rings, submitted.

Al-Zoubi, K., Jaradat, M. and Abu-Dawwas, R., On graded classical prime and graded prime submodules, Bull. Iranian Math. Soc., 41 (1), 217-225, (2015).

Al-Zoubi, K. and Qarqaz, F., An intersection condition for graded prime submodules in Gr multiplication modules, Math. Reports, 20 (3), 329–336, (2018).

Atani, S. E., On graded prime submodules, Chiang Mai J. Sci., 33 (1), 3-7, (2006).

Atani, S. E., and Atani, R. E., Graded multiplication modules and the graded ideal g(M), Turk. J. Math., 33, 1-9, (2009).

Atani, S. E., and Farzalipour, F., Notes on the graded prime submodules, Int. Math. Forum 1, 38, 1871-1880, (2006).

Atani, S. E. and Saraei, F. E. K., Graded Modules which Satisfy the Gr-Radical Formula, Thai J. Math., 8 (1), 161-170, (2010).

Atani, S. E. and Farzalipour, F., On graded secondary modules, Turk. J. Math., 31, 371-378, (2007).

Escoriza, J. and Torrecillas, B., Multiplication Objects in Commutative Grothendieck Categories, Comm. in Algebra, 26 (6), 1867-1883, (1998).

Ghiasvand, P. and Farzalipour, F., On Graded Primary Submodules of Graded Multiplication Modules, Int. J. Alg., 4 (9), 429-434, (2010).

Hazrat, R., Graded Rings and Graded Grothendieck Groups, Cambridge University Press, Cambridge, (2016).

Lee, S. C. and Varmazyar, R., Semiprime submodules of Graded multiplication modules, J. Korean Math. Soc., 49 (2), 435-447, (2012).

C. Nastasescu and V.F. Oystaeyen, Graded and filtered rings and modules. Lecture notes in mathematics 758, Berlin-New York: Springer-Verlag, (1982).

Nastasescu, C. and Van Oystaeyen, F., Graded Ring Theory, Mathematical Library 28, North Holand, Amsterdam, (1982).

Nastasescu, C. and Van Oystaeyen, F., Methods of Graded Rings, LNM 1836. Berlin-Heidelberg: Springer-Verlag, (2004).

Oral, K. H. Tekir, U. and Agargun, A. G., On Graded prime and primary submodules, Turk. J. Math., 35, 159-167, (2011).

Refai, M. and Al-Zoubi, K., On graded primary ideals, Turk. J. Math., 28, 217-229, (2004).

Refai, M., Hailat, M. and Obiedat, S., Graded radicals on graded prime spectra, Far East J. of Math. Sci., part I, 59-73, (2000).

Tavallaee, H. A. and Zolfaghari, M., Graded weakly semiprime submodules of graded multiplication modules, Lobachevskii J. Math., 34 (1), 61-67, (2013).

Varmazyar, R.,Graded coprime submodules, Math. Sci., 6(1), Art. 70, 4 pp., (2012).

Zamani, N., Finitely generated graded multiplication modules, Glasgow Math. J., 53(3), 693-705, (2011).