2020
DOI: 10.24330/ieja.768206
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Different Types of G-Prime Ideals Associated to a Graded Module and Graded Primary Decomposition in a Graded Prüfer Domain

Abstract: In this paper, we introduce the notion of graded Prüfer domain as a generalization of Prüfer domain to the graded case. We generalize several types of prime ideals associated to a module over a ring to the graded case and prove that most of them coincide over a graded Prüfer domain. Moreover, we investigate the graded primary decomposition of graded ideals in a graded Prüfer domain under certain conditions and give some applications of it.

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Cited by 1 publication
(3 citation statements)
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References 13 publications
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“…[7] Let M be a G-graded A-module and N be a graded submodule of M . Then (1) The graded radical of N is denoted by Gr(N ) and defined as the ideal of A generated by the set {a ∈ h(A) :…”
Section: Preliminariesmentioning
confidence: 99%
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“…[7] Let M be a G-graded A-module and N be a graded submodule of M . Then (1) The graded radical of N is denoted by Gr(N ) and defined as the ideal of A generated by the set {a ∈ h(A) :…”
Section: Preliminariesmentioning
confidence: 99%
“…[1, Definition 3.1] Let A be a G-graded integral domain. Then (1) A is said to be a G-graded valuation domain if for any x, y ∈ h(A), either x divides y or y divides x. (2) A is said to be a G-graded Prüfer domain if its graded localization A G p is a G-graded valuation domain for each G-prime ideal P of A.…”
Section: Applications Of G-attached Prime Idealsmentioning
confidence: 99%
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