On graded primary-like submodules of graded modules over graded commutative rings
DOI:
https://doi.org/10.22199/issn.0717-6279-3467Keywords:
Graded primary ideals, Graded primary-like submodules, Graded prime submodules, gr-primeful propertyAbstract
Let G be a group with identity e. Let R be a G-graded commutative ring andM a graded R-module. In this paper, we introduce the concept of graded primary-like submodules as a new generalization of graded primary ideals and give some basic results about graded primary-like submodules of graded modules. Special attention has been paid, when graded submodules satisfies the gr-primeful property, to and extra properties of these graded submodules.
Downloads
References
K. Al-Zoubi, “The graded primary radical of a graded submodules”, Analele ştiinţifice ale Universităţii "Al.I. Cuza" din Iaşi. Matematică (Online), vol. 1, no. 2, pp. 395-402, 2016. [On line]. Available: https://bit.ly/36f5e3s
K. Al-Zoubi and R. Abu-Dawwas, “On graded quasi-prime submodules”, Kyungpook mathematical journal, vol. 55, no. 2, pp. 259-266, 2015. http://dx.doi.org/10.5666/KMJ.2015.55.2.259
K. Al-Zoubi, R. Abu-Dawwas and I. Al-Ayyoub, “Graded semiprime submodules and graded semi-radical of graded submodules in graded modules”, Ricerche di matematica, vol. 66, no. 2, pp. 449-455, 2017. https://doi.org/10.1007/s11587-016-0312-x
K. Al-Zoubi and M. Al-Dolat, “On graded classical primary submodules”, Advances in pure and applied mathematics, vol. 7, no. 2, pp. 93-96, 2016. https://doi.org/10.1515/apam-2015-0021
K. Al-Zoubi, M. Jaradat and R. Abu-Dawwas, “On graded classical prime and graded prime submodules”, Bulletin of the Iranian Mathematical Society, vol. 41, no. 1, pp. 217-225, 2015. [On line]. Available: https://bit.ly/2TB9K9Y
K. Al-Zoubi and F. Qarqaz, “An intersection condition for graded prime submodules in Gr-multiplication modules”, Mathematicals reports, vol. 20, no. 3, pp. 329-336, 2018. [On line]. Available: https://bit.ly/2TL9KUC
S. E. Atani, “On graded prime submodules”, Chiang mai journal of science, vol. 33, no. 1, pp. 3-7, 2006. [On line]. Available: https://bit.ly/3wmHTYr
S. E. Atani and R. E. Atani, “Graded multiplication modules and the graded ideal θg(M)”, Turkish journal of mathematics, vol. 35, no. 1, pp. 1-9, 2009. https://doi.org/10.3906/mat-0901-22
S. E. Atani and F. Farzalipour, “Notes on the graded prime submodules”, International mathematical forum, vol. 1, no. 38, pp. 1871-1880, 2006. http://dx.doi.org/10.12988/imf.2006.06162
S. E. Atani and F. E. K. Saraei, “Graded modules which satisfy the Gr-radical formula”, Thai journal of mathematics , vol. 8, no. 1, pp. 161-170, 2010. [On line]. Available: https://bit.ly/3e8mZWL
S. E. Atani and F. Farzalipour, “On graded secondary modules”, Turkish journal of mathematics, vol. 31, no. 4, pp. 371-378, 2007. [On line]. Available: https://bit.ly/3yt7wbh
J. Escoriza and B. Torrecillas, “Multiplication objects in commutative Grothendieck categories”, Communications in algebra, vol. 26, no. 6, pp. 1867-1883, 1998. https://doi.org/10.1080/00927879808826244
P. Ghiasvand and F. Farzalipour, “On graded primary submodules of graded multiplication modules”, International journal of algebra, vol. 4, no. 9, pp. 429-434, 2010. [On line]. Available: https://bit.ly/3wgHirb
R. Hazrat, Graded rings and graded Grothendieck groups, Cambridge: Cambridge University Press, 2016. https://doi.org/10.1017/CBO9781316717134
C. P. Lu, “A module whose prime spectrum has the surjective natural map”, Houston journal of mathematics, vol. 33, no. 1, pp. 125-143, 2007. [On line]. Available: https://bit.ly/36f7F68
S.C. Lee and R. Varmazyar, “Semiprime submodules of graded multiplication modules”, Journal of the Korean Mathematical Society, vol. 49, no. 2, pp. 435-447, 2012. https://doi.org/10.4134/JKMS.2012.49.2.435
H. F. Moghimi and F. Rashedi, “Primary-like submodules satisfying the primeful property”, Transactions on Algebra and its Applications, vol. 1, pp. 43-54, 2015.
C. Nastasescu and .F. Oystaeyen, Graded and filtered rings and modules. Berlin: Springer, 1979. https://doi.org/10.1007/BFb0067331
C. Nastasescu, F. Oystaeyen, Graded ring theory, Amsterdam: North Holland, 1982.
C. Nastasescu and F. Oystaeyen, Methods of graded rings. Berlin: Springer, 2004. https://doi.org/10.1007/b94904
K. H. Oral, U. Tekir and A.G. Agargun, “On Graded prime and primary submodules”, Turkish journal of mathematics, vol. 35, no. 2, pp. 159-167, 2011. https://doi.org/10.3906/MAT-0904-11
M. Refai and K. Al-Zoubi, “On graded primary ideals”, Turkish journal of mathematics, vol. 28, no. 3, pp. 217-229, 2004. [On line]. Available: https://bit.ly/3hMUvTs
M. Refai, M. Hailat and S. Obiedat, “Graded radicals on graded prime spectra”, Far East journal of mathematical sciences, vol. 1, no. 1, pp. 59-73, 2000.
H. A. Tavallaee and M. Zolfaghari, “Graded weakly semiprime submodules of graded multiplication modules”, Lobachevskii journal of mathematics, vol. 34, no. 1, pp. 61-67, 2013. https://doi.org/10.1134/S1995080213010113
Downloads
Published
Issue
Section
License
Copyright (c) 2021 Khaldoun Falah Al-Zoubi, Mohammed Al-Dolat
This work is licensed under a Creative Commons Attribution 4.0 International License.
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.