DIFFERENT TYPES OF G-PRIME IDEALS ASSOCIATED TO A GRADED MODULE AND GRADED PRIMARY DECOMPOSITION IN A GRADED PRÜFER DOMAIN

Authors : Ajim Uddin ANSARI, B K SHARMA, Shiv Datt KUMAR

Pages : 141-155

Doi:10.24330/ieja.768206

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Publication Date : 2020-07-14

Article Type : Research Paper

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. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$
Keywords : Graded ring, graded module, graded Prüfer domain, graded primary decomposition