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In this paper, we introduce the notion of graded Prufer domain as a generalization of Prufer 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 Prufer domain. Moreover, we investigate the graded primary decomposition of graded ideals in a graded Prufer domain under certain conditions and give some applications of it. $$

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