On graded 2-classical prime submodules of graded modules over graded commutative rings
DOI:
https://doi.org/10.22199/issn.0717-6279-2019-04-0049Keywords:
Graded 2-classical prime submodule, Graded classical prime submodule, Graded prime submoduleAbstract
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 2-classical prime submodules. Various properties of graded 2-classical prime submodules are considered.
References
K. Al-Zoubi and R. Abu-Dawwas, “On graded 2-absorbing and weakly graded 2-absorbing submodules”, Journal of mathematical sciences: advances and applications, vol. 28, pp. 45- 60, 2014. [On line]. Available: https://bit.ly/2Jk4xuT
K. Al-Zoubi and R. Abu-Dawwas, “On graded quasi-prime submodules”, Kyungpook mathematical journal, vol. 55, no. 2, pp. 259-266, Jun. 2015. [On line]. Available: https://bit.ly/2MUtm19
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/2MteIz8
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, doi: 10.1515/apam-2015-0021.
K. Al-Zoubi and F. Qarqaz, “An intersection condition for graded prime submodules”, Mathematical reports, vol. 20, no. 3, pp. 329-336, 2018. [On line]. Available: https://bit.ly/2P27ELB
S. Atani, “On graded prime submodules”, Chiang Mai journal of science, vol. 33, no. 1, pp. 3-7, 2006. [On line]. Available: https://bit.ly/2o0Ab9b
S. Atani, “On graded weakly prime ideals”, Turkish journal of mathematics, vol. 30, no. 4, pp. 351-358, 2006. [On line]. Available: https://bit.ly/2Btfiqm
S. 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/2J3xgE3
P. Deligne, P. Etingof, D. Freed, L. Jeffrey, D. Kazhdan, J. Morgan, D. Morrison, and E. Witten, Eds., Quantum fields and strings: a course for mathematicians. Providence, RI: American Mathematical Society, 1999.
A. Darani and S. Motmaen,” Zariski topology on the spectrum of graded classical prime submodules”, Applied general topology, vol. 14, no. 2, pp. 159-169, 2013, doi: 10.4995/agt.2013.1586.
I. Kolar, P. Michor, and J. Slovak, Natural operations in differential geometry, Berlin: Springer, 2010, doi: 10.1007/978-3-662-02950-3.
R. Hazrat, Graded rings and graded grothendieck groups, vol. 435. Cambridge: Cambridge University Press, 2016, doi: 10.1017/CBO9781316717134.
C. Năstăsescu and F. Van Oystaeyen, Graded and filtered rings and modules, vol. 758. Berlin: Springer, 1979, doi: 10.1007/BFb0067331.
C. Năstăsescu and F. Van Oystaeyen, Graded ring theory, vol. 28. Amsterdam: Elsevier, 1982. [On line]. Available: https://bit.ly/2BrtNLm
C. Năstăsescu and F. Van Oystaeyen, Methods of graded rings, vol. 1836. Berlin: Springer, 2004, doi: 10.1007/b94904.
K. Oral, U. Tekir and A. Agargun, “On graded prime and primary submodules”, Turkish journal of mathematics, vol. 35, no. 2, pp. 159-167, 2011. [On line]. Available: https://bit.ly/2VUgdJA
A. Rogers, Supermanifolds: theory and applications. Singapore: World Scientific, 2007, doi:10.1142/1878 .
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/2VYd63f
M. Refai, M. Hailat and S. Obiedat, “Graded radicals on graded prime spectra”, Far East journal of mathematical sciences, vol. 1, pp. 59-73, 2000.
R. Uregen, U. Tekir and K. Oral, “On the union of graded prime ideals”, Open physics, vol. 14, no. 1 pp. 114-118, 2016, doi: 10.1515/phys-2016-0011.
Published
How to Cite
Issue
Section
-
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.