Graded $\delta$-primary structures
Résumé
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.
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Références
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.
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