Graded uniformly $pr$-ideals
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Let $R$ be a $G$-graded commutative ring with a nonzero unity and $P$ be a proper graded ideal of $R$. Then $P$ is said to be a graded uniformly $pr$-ideal of $R$ if there exists $n\in \mathbb{N}$ such that whenever $a, b\in h(R)$ with $ab\in P$ and $Ann(a)=\{0\}$, then $b^{n}\in P$. The smallest such $n$ is called the order of $P$ and is denoted by $ord_{R}(P)$. In this article, we study the characterizations on this new class of graded ideals, and investigate the behaviour of graded uniformly $pr$-ideals in graded factor rings and in direct product of graded rings.
Abstract
Let $R$ be a $G$-graded commutative ring with a nonzero unity and $P$ be a proper graded ideal of $R$. Then $P$ is said to be a graded uniformly $pr$-ideal of $R$ if there exists $n\in \mathbb{N}$ such that whenever $a, b\in h(R)$ with $ab\in P$ and $Ann(a)=\{0\}$, then $b^{n}\in P$. The smallest such $n$ is called the order of $P$ and is denoted by $ord_{R}(P)$. In this article, we study the characterizations on this new class of graded ideals, and investigate the behaviour of graded uniformly $pr$-ideals in graded factor rings and in direct product of graded rings.
참고문헌 (11)
- R. Abu-Dawwas, "Graded semiprime and graded weakly semiprime ideals", Ital. J. Pure Appl. Math, (36), pp.535~542 (2016)
- Rashid Abu-Dawwas, "ON GRADED SEMI-PRIME RINGS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 20(1), pp.19~22 (2017), 장전수학회[DOI]
- R. Abu-Dawwas, "Graded r-ideals", Iran. J. Math. Sci. Inform, 14(2), pp.1~8 (2019), Department of Mathematics, Hokkaido University[DOI]
- K. Al-Zoubi, "On graded 2-absorbing and graded weakly 2-absorbing ideals", Hacet. J. Math. Stat, 48(4), pp.724~731 (2018), Hacettepe University[DOI]
- Khaldoun Al-Zoubi, "On graded classical primary submodules", Advances in Pure and Applied Mathematics, 7(2), pp.93~96 (2016), ISTE Group[DOI]
- M. Bataineh, "Graded almost 2-absorbing structures", JP J. Algebra, Number Theory Appl, 39(1), pp.63~75 (2017)
- R. Gilmer, "Multiplicative Ideal Theory" (1972), Marcel Dekker, Inc
- C. N˘ast˘asescu, "Methods of graded rings" (2004), Springer-Verlag
- D. G. Northcott, "Lessons on Rings, Modules and Multiplicities" (1968), Cambridge University Press
- M. Refai, "On graded primary ideals", Turkish J. Math, 28(3), pp.217~229 (2004)
- M. B. Rege, "Armendariz rings", Proc. Japan Acad. Ser. A Math. Sci, 73(1), pp.14~17 (1997)[DOI]