Graded $\delta$-primary structures
Resumo
Let $G$ be a group with identity $e$, $R$ a $G$-graded commutative ring with unity $1$ and $M$ a $G$-graded $R$-module. In this article, we unify the concepts of graded prime ideals and graded primary ideals into a new concept, namely, graded $\delta$-primary ideals. Also, we unify the concepts of graded $2$-absorbing ideals and graded $2$-absorbing primary ideals into a new concept, namely, graded $2$-absorbing $\delta$-primary ideals. A number of results about graded prime, graded primary, graded $2$-absorbing and graded $2$-absorbing primary ideals are extended into these new structures. Finally, we extend the concept of graded $\delta$-primary ideals into graded $\delta$-primary submodules. A number of results about graded prime, graded primary submodules are extended into this new structure.
Downloads
Referências
R. Abu-Dawwas, Multiplication components of graded modules, Italian Journal of Pure and Applied Mathematics, 35 (2015), 389-392.
R. Abu-Dawwas, Graded semiprime and graded weakly semiprime ideals, Italian Journal of Pure and Applied Mathematics, 36 (2016), 535-542.
R. Abu-Dawwas, Graded semiprime multiplication modules, accepted in the Boletim Sociedaded Paranaense de Matematica.
R. Abu-Dawwas and K. Al-Zoubi, On graded weakly classical prime submodules, Iranian Journal of Mathematical Sciences and Informatics, 12 (1) (2017), 153-161.
R. Abu-Dawwas, M. Bataineh and M. Al-Muanger, Graded prime submodules over non-commutative rings, Vietnam Journal of Mathematics, 46 (3) (2018), 681-692. https://doi.org/10.1007/s10013-018-0274-2
R. Abu-Dawwas and M. Refai, Some remarks on graded weak multiplication modules, Journal of Contemporary Mathematical Sciences, 6 (14) (2011), 681-686.
R. Abu-Dawwas and M. Refai, Some remarks on Re-multiplication modules over first strongly graded rings, East-West Fournal of Mathematics, 13 (1) (2011), 57-61.
K. Al-Zoubi, R. Abu-Dawwas and S. Ceken, On graded 2-absorbing and graded weakly 2-absorbing ideals, Hacettepe Journal of Mathematics and Statistics 48 (3) (2019), 724-731. https://doi.org/10.15672/HJMS.2018.543
K. Al-Zoubi and N. Sharafat, On graded 2-absorbing primary and graded weakly 2-absorbing primary ideals, Journal of the Korean Mathematical Society, 54 (2) (2017), 675-684. https://doi.org/10.4134/JKMS.j160234
S. E. Atani, On graded prime submodules, Chiang Mai Journal of Science, 33 (1) (2006), 3-7.
S. E. Atani and F. Farzalipour, On graded secondary modules, Turkish Journal of Mathematics, 31 (2007), 371-378.
J. Escoriza and B. Toeercillas, Multiplication objects in Commutative Grothendieck category, Communications in Algebra, 16 (1998), 1867-1883. https://doi.org/10.1080/00927879808826244
B. Fahid and Z. Dongsheng, 2-Absorbing δ-primary ideals in commutative rings, Kyungpook Mathematical Journal, 57 (2) (2017), 193-198.
F. Farzalipour and P. Ghiasvand, On the union of graded prime submodules, Thai Journal of Mathematics, 9 (1) (2011), 49-55. https://doi.org/10.5402/2011/939687
F. Farzalipour and P. Ghiasvand, On graded semiprime and graded weakly semiprime ideals, International Electronic Journal of Algebra, 13 (2013), 15-22.
S. Koc, R. N. Uregen and U Tekir, On 2-absorbing quasi primary submodules, Filomat, 31 (10) (2017), 2943-2950. https://doi.org/10.2298/FIL1710943K
C. Nastasescu and F. V. Oystaeyen, Methods of graded rings, Lecture Notes in Mathematics, 1836, Springer-Verlag, Berlin, (2004). https://doi.org/10.1007/b94904
D. G. Northcott, Lessons on rings, modules and multiplicities, Cambridge University Press, 1968. https://doi.org/10.1017/CBO9780511565922
K. H. Oral, U. Tekir and A. G. Agargun, On graded prime and primary submodules, Turkish Journal of Mathematics, 35 (2011), 159-167.
M. Refai, M. Hailat and S. Obiedat, Graded radicals and graded prime spectra, Far East Journal of Mathematical Sciences, (2000), 59-73.
G. Ulucak, U. Tekir and S. Koc, On n-absorbing δ-primary ideals, Turkish Journal of Mathematics, 42 (4) (2018), 1833-1844. https://doi.org/10.3906/mat-1710-3
R. N. Uregen, U. Tekir, K. P. Shum and S. Koc, On Graded 2-Absorbing Quasi Primary Ideals, Southeast Asian Bulletin of Mathematics, 43 (4) (2019), 601-613.
Copyright (c) 2022 Boletim da Sociedade Paranaense de Matemática

This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).