On properties of graded rings and graded modules
DOI:
https://doi.org/10.22199/issn.0717-6279-4814Keywords:
weakly graded rings, weakly crossed products, invertible graded rings, graded semi-essential submodules, graded essential sub-modules, graded uniform modules, graded semi-uniform modulesAbstract
Let R be a G-graded ring. In this article, we introduce two new concepts on graded rings, namely, weakly graded rings and invertible graded rings, and we discuss the relations between these concepts and several properties of graded rings. Also, we study the concept of weakly crossed products and study some properties defined on weakly crossed product and give the relationship between this new concept and several properties of graded rings. Moreover, in this article, we give a generalization for the concept of graded essential submodules, and introduce the concept of graded semi-uniform modules which is a generalization for the concept of graded uniform modules.
References
R. Abu-Dawwas, “On graded semi-prime rings”, Proceedings of the Jangjeon Mathematical Society, vol. 20, no. 1, pp. 19-22, 2017.
R. Abu-Dawwas, “Multiplication Components of graded modules”, Italian Journal of Pure and Applied Mathematics, vol. 35, pp. 389-392, 2015. [On line]. Available: https://bit.ly/3hf9Yz0
R. Abu-Dawwas, “More on crossed product over support of graded rings”, International Mathematical Forum, vol. 5, no. 63, pp. 3121-3126, 2010. [On line]. Available: https://bit.ly/3UxbSsO
R. Abu-Dawwas, K. Al-Zoubi, and M. Bataineh, “Prime submodules of graded modules”, Proyecciones (Antofagasta), vol. 31, no. 4, pp. 355–361, 2012. https://doi.org/10.4067/s0716-09172012000400004
R. Abu-Dawwas and M. Refai, “Some remarks on R e-multiplication modules over first strongly graded rings”, East-West Journal of Mathematics, vol. 13, no. 1, pp. 57-61, 2011. [On line]. Available: https://bit.ly/3Wz4K15
R. Abu-Dawwas and M. Refai, “Further results on graded prime submodules”, International Journal of Algebra, vol. 4, no. 28, pp. 1413-1419, 2010. [On line]. Available: https://bit.ly/3hgSZvU
S. Çeken and M. Alkan, “On graded second and Coprimary modules and graded secondary representations”, Bulletin of the Malaysian Mathematical Sciences Society, vol. 38, no. 4, pp. 1317–1330, 2014. https://doi.org/10.1007/s40840-014-0097-6
E. C. Dade, “Compounding clifford’s theory”, Annals of Mathematics, Second Series, vol. 91, no. 1, pp. 236-290, 1970. https://doi.org/10.2307/1970606
S. Ebrahimi Atani, “On graded prime submodules”, Chiang Mai Journal of Science, vol. 33, no. 1, pp. 3-7, 2006. [On line]. Available: https://bit.ly/3FN8mqg
J. Escoriza and B. Torrecillas, “Multiplication objects in commutative Grothendieck category”, Communications in Algebra, vol. 26, pp. 1867-1883, 1998. https://doi.org/10.1080/00927879808826244
F. Farzalipour and P. Ghiasvand, “On graded weak multiplication modules”, Tamkang Journal of Mathematics, vol. 43, no. 2, pp. 171-177, 2012. https://doi.org/10.5556/j.tkjm.43.2012.171-177
F. Farzalipour and P. Ghiasvand, “On the union of graded prime submodules”, Thai Journal of Mathematics, vol. 9, no. 1, pp. 49-55, 2011.
K. Khaksari and F. R. Jahromi, “Multiplication graded modules”, International Journal of Algebra, vol. 7, no. 1, pp. 17-24, 2013. https://doi.org/10.12988/ija.2013.13003
C. Nastasescu and F. Van Oystaeyen, Methods of graded rings. Berlin: Springer, 2004.
M. Refai, “Various types of strongly graded rings”. Abhath Al-Yarmouk Journal (Pure Sciences and Engineering Series), vol. 4, no. 2, pp. 9-19, 1995.
M. Refai and R. Abu-Dawwas, “Grade fixing maps”, International Journal of Algebra, vol. 4, no. 19, pp. 939-944, 2010. [On line]. Available: https://bit.ly/3T3MQRa
M. Refai, M. Hailat and S. Obiedat, “Graded radicals and graded prime spectra”, Far East Journal of Mathematical Sciences, pp. 59-73, 2000.
M. Refai and F. Moh’d, “First strongly graded modules”, International Journal of Mathematics (Game Theory and Algebra), vol. 15, no. 4, pp. 451-457, 2006.
Published
How to Cite
Issue
Section
Copyright (c) 2022 Mashhoor Refai, Rashid Abu-Dawwas
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.
