Almost graded multiplication and almost graded comultiplication modules

• Autorzy: Bataineh Malik , Abu-Dawwas Rashid , Shtayat Jenan

Identyfikatory

DOI

10.1515/dema-2020-0023

• Języki publikacji: EN

Abstrakty

EN

Let G be a group with identity e, R be a G-graded commutative ring with a nonzero unity 1 and M be a G-graded R-module. In this article, we introduce and study the concept of almost graded multiplication modules as a generalization of graded multiplication modules; a graded R-module M is said to be almost graded multiplication if whenever a ∈ h(R) satisfies AnnR (aM) = AnnR (M), then (0 :M a) = {0}. Also, we introduce and study the concept of almost graded comultiplication modules as a generalization of graded comultiplication modules; a graded R-module M is said to be almost graded comultiplication if whenever a ∈ h(R) satisfies AnnR (aM) = AnnR (M), then aM = M. We investigate several properties of these classes of graded modules.

Słowa kluczowe

EN

graded multiplication module; graded comultiplication module

PL

moduły mnożenia; stopniowanie modułów; teoria modułów

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2020
• Tom: Vol. 53, nr 1
• Strony: 325--331
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Bataineh Malik

• Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan

autor

Abu-Dawwas Rashid

• Department of Mathematics, Yarmouk University, Irbid, Jordan

autor

Shtayat Jenan

• Department of Mathematics, Yarmouk University, Irbid, Jordan

Bibliografia

• [1] C. Nastasescu and F. van Oystaeyen, Methods of Graded Rings, Lecture Notes in Mathematics, vol. 1836, Springer-Verlag, Berlin, 2004.
• [2] F. Farzalipour and P. Ghiasvand, On the union of graded prime submodules, Thai J. Math. 9(2011), no. 1, 49-55.
• [3] J. Escoriza and B. Torrecillas, Multiplication objects in commutative Grothendieck category, Comm. Algebra 26(1998), 1867-1883.
• [4] K. Khaksari and F. R. Jahromi, Multiplication graded modules, Internat. J. Algebra 7(2013), no. 1, 17-24.
• [5] S. E. Atani, On graded prime submodules, Chiang Mai J. Sci.33(2006), no. 1, 3-7.
• [6] F. Farzalipour and P. Ghiasvand, On graded weak multiplication modules, Tamkang J. Math. 43(2012), no. 2, 171-177.
• [7] S. C. Lee and R. Varmazyar, Semiprime submodules of graded multiplication modules, J. Korean Math. Soc. 49(2012), no. 2, 435-447.
• [8] F. Farzalipour and P. Ghiasvand, On graded semiprime submodules, Int. J. Math. Comput. Phys. Electr. Comp. Eng. 6(2012), no. 8, 1169-1172.
• [9] R. Abu-Dawwas, Graded semiprime multiplication modules, Bol. Soc. Parana. Mat., (accepted).
• [10] S. E. Atani, On graded weakly prime submodules, Int. Math. Forum 1(2006), no. 2, 61-66.
• [11] R. Abu-Dawwas, H. Saber, T. Alraqad, and R. Jaradat, On generalizations of graded multiplication modules, Bol. Soc. Parana. Mat., (accepted). DOI: 10.5269/bspm.51241.
• [12] K. Al-Zoubi and R. Abu-Dawwas, On graded 2-absorbing and weakly graded 2-absorbing submodules, J. Math. Sci. Adv. Appl. 28(2014), 45-60.
• [13] M. Hamoda and A. E. Ashour, On graded n-absorbing submodules, Le Matematiche LXX (2015), 243-254.
• [14] F. Farshadifar and H. Ansari-Toroghy, Quasi-multiplication and quasi-comultiplication modules, Jordan J. Math. Stat. 13(2020), no. 1, 125-137.
• [15] H. Ansari-Toroghy and F. Farshadifar, Graded comultiplication modules, Chiang Mai J. Sci. 38(2011), no. 3, 311-320.
• [16] R. Abu-Dawwas, M. Bataineh and A. Da’keek, Graded weak comultiplication modules, Hokkaido Math. J. 48(2019), 253-261.
• [17] S. A. Balde, M. F. Maaouia and A. O. Chbih, Hopfian and cohopfian objects in the categories of Gr(A–Mod) and Comp(Gr(A–Mod)), J. Math. Res. 12(2020), no. 2, 17-27.
• [18] H. Ansari-Toroghy and F. Farshadifar, On graded second modules, Tamkang J. Math. 43(2012), no. 4, 499-505.
• [19] S. Çeken and M. Alkan, On graded second and coprimary modules and graded second representations, Bull. Malays. Math. Sci. Soc. 38(2015), no. 4, 1317-1330.
• [20] J. Chen and Y. Kim, Graded irreducible modules are irreducible, Comm. Algebra 45(2017), no. 5, 1907-1913.
• [21] C. Meng, G-graded irreducibility and the index of reducibility, Comm. Algebra 48(2020), no. 2, 826-832.