On graded $(m, n)$-closed submodules
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Let $A$ be a $G$-graded commutative ring with identity and $M$ a graded $A$-module. Let $m, n$ be positive integers with $m>n$. A proper graded submodule $L$ of $M$ is said to be graded $(m, n)$-closed if $a^{m}_g\cdot x_t\in L$ implies that $a^{n}_g\cdot x_t\in L$, where $a_g\in h(A)$ and $x_t\in h(M)$. The aim of this paper is to explore some basic properties of these class of submodules which are a generalization of graded $(m, n)$-closed ideals. Also, we investigate $GC^{m}_n-rad$ property for graded submodules.
Abstract
Let $A$ be a $G$-graded commutative ring with identity and $M$ a graded $A$-module. Let $m, n$ be positive integers with $m>n$. A proper graded submodule $L$ of $M$ is said to be graded $(m, n)$-closed if $a^{m}_g\cdot x_t\in L$ implies that $a^{n}_g\cdot x_t\in L$, where $a_g\in h(A)$ and $x_t\in h(M)$. The aim of this paper is to explore some basic properties of these class of submodules which are a generalization of graded $(m, n)$-closed ideals. Also, we investigate $GC^{m}_n-rad$ property for graded submodules.
참고문헌 (11)
- K. Al-Zoubi, "Graded semiprime submodules and graded semi-radical of graded submodules in graded modules", Ric. Mat, 66(2), pp.449~455 (2017)[DOI]
- D. F. Anderson, "On (m, n)-closed ideals of commutative rings", J. Algebra Appl, 16(1), pp.1750013~1750033 (2017)[DOI]
- S. E. Atani, "On graded prime submodules", Chiang Mai J. Sci, 33(1), pp.3~7 (2006)
- 이상철, "Semiprime submodules of graded multiplication modules", 대한수학회지, 49(2), pp.435~447 (2012), 대한수학회
- S. C. Lee, "Semiprime submodules of a module and related concepts", J. Algebra Appl, 18(8), pp.1950147~1950157 (2019)[DOI]
- C. N˘ast˘asescu, "Graded and filtered rings and modules", Lecture Notes in Mathematics, 758 (1979), Springer
- C. N˘ast˘asescu, "Graded Ring Theory, North-Holland Mathematical Library, 28" (1982), North-Holland
- A. Pekin, "(m, n)-semiprime submodules", Proc. Est. Acad. Sci, 70(3), pp.260~267 (2021)[DOI]
- H. Saber, "On graded s-prime submodules", AIMS Math, 6(3), pp.2510~2524 (2021)[DOI]
- B. Sara¸c, "On semiprime submodules", Comm. Algebra, 37(7), pp.2485~2495 (2009)[DOI]
- R. Varmazyar, "Graded coprime submodules", Math. Sci, 6, pp.70~73 (2012), Springer[DOI]