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arXiv · 2305.19633

How many ideals whose quotient rings are Gorenstein exist?

Naoki Endo
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Abstract

For an Ulrich ideal in a Gorenstein local ring, the quotient ring is again Gorenstein. Aiming to further develop the theory of Ulrich ideals, this paper investigates a naive question of how many non-principal ideals whose quotient rings are Gorenstein exist in a given Gorenstein ring. The main result provides that the number of such graded ideals in a symmetric numerical semigroup ring $R$ coincides with the conductor of the semigroup. We furthermore provide a complete list of non-principal graded ideals $I$ in $R$ whose quotient rings $R/I$ are Gorenstein.

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Naoki Endo. 2023-05-31. How many ideals whose quotient rings are Gorenstein exist?. https://arxiv.org/abs/2305.19633

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