Homogeneous prime elements in normal two-dimensional graded rings

2018/07/08 by Singh, Anurag K., Takahashi, Ryo, Watanabe, Kei-ichi
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.02738

Abstract

We prove necessary and sufficient conditions for the existence of homogeneous prime elements in normal N-graded rings of dimension two, in terms of rational coefficient Weil divisors on projective curves.

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• Factorially graded rings and Cox rings
• Some Results On Normal Homogeneous Ideals
• On Gelfand graded commutative rings
• Bounds on the number of generators of prime ideals
• Homogeneity of zero-divisors, units and colon ideals in a graded ring