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Decompositions of graded maximal submodules
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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.
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.
참고문헌 (9)
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- S. Ebrahimi Atani, "Notes on the graded prime submodules", International Mathematical Forum, (37-40), pp.1871~1880 (2006), Hikari, Ltd.[DOI]
- J. Escoriza, "Multiplication objects in commutative grothendieck categories", Communications in Algebra, 26(6), pp.1867~1883 (1998), Informa UK Limited[DOI]
- R. Hazrat, "Graded rings and graded Grothendieck groups" (2016), Cambridge University Press
- F. Moh'd amd M. Khader, "Graded modules over first strongly graded rings", Malaysian J. Math. Sci, 11(2), pp.20520~ (2017)
- C. Nastasescu, "Methods of graded rings" (2004), Springer-Verlag
- M. Refai, "First strongly graded modules", Int. J. Math. Game Theory Algebra, 15(4), pp.451~457 (2006)
- M. Refai, "More properties on various types of strongly graded rings", Pac. -Asian J. Math, 1(2), pp.129~135 (2007)
- M. Refai, "On exible graded modules", Ital. J. Pure Appl. Math., (22), pp.125~132 (2007)
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