[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c200428

DECOMPOSITIONS OF GRADED MAXIMAL SUBMODULES

Moh'd, Fida (Department of Basic Sciences Princess Sumaya University for Technology)

Publication Information

Communications of the Korean Mathematical Society / v.37, no.1, 2022 , pp. 1-15 More about this Journal

Abstract

In this paper, we present different decompositions of graded maximal submodules of a graded module. From these decompositions, we derive decompositions of the graded Jacobson radical of a graded module. Using these decompositions, we prove new theorems about graded maximal submodules, improve old theorems, and give other proofs for old theorems.

Keywords

Graded rings; graded modules; graded maximal submodules; gr-maximal submodules; graded Jacobson radical; gr-Jacobson radical; gr-max-nested modules; decomposition;

Citations & Related Records

Reference

1	C. Nastasescu and F. Van Oystaeyen, Methods of graded rings, Lecture Notes in Mathematics, 1836, Springer-Verlag, Berlin, 2004. https://doi.org/10.1007/b94904 DOI
2	M. Refai and F. A. M. Moh'd, On flexible graded modules, Ital. J. Pure Appl. Math. No. 22 (2007), 125-132.
3	E. C. Dade, Group-graded rings and modules, Math. Z. 174 (1980), no. 3, 241-262. https://doi.org/10.1007/BF01161413 DOI
4	S. Ebrahimi Atani and F. Farzalipour, Notes on the graded prime submodules, Int. Math. Forum 1 (2006), no. 37-40, 1871-1880. https://doi.org/10.12988/imf.2006.06162 DOI
5	J. Escoriza and B. Torrecillas, Multiplication objects in commutative Grothendieck categories, Comm. Algebra 26 (1998), no. 6, 1867-1883. https://doi.org/10.1080/00927879808826244 DOI
6	R. Hazrat, Graded rings and graded Grothendieck groups, London Mathematical Society Lecture Note Series, 435, Cambridge University Press, Cambridge, 2016. https://doi.org/10.1017/CBO9781316717134 DOI
7	F. Moh'd amd M. Khader, Graded modules over first strongly graded rings, Malaysian J. Math. Sci. 11 (2017), no. 2, 20520.
8	M. Refai and F. A. M. Moh'd, First strongly graded modules, Int. J. Math. Game Theory Algebra 15 (2006), no. 4, 451-457.
9	M. Refai and F. A. M. Moh'd, More properties on various types of strongly graded rings, Pac.-Asian J. Math. 1 (2007), no. 2, 129-135.