How many ideals whose quotient rings are Gorenstein exist?

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 resul...

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Bibliographic Details
Published inarXiv.org
Main Author Endo, Naoki
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 29.08.2024
Subjects
Quotients
Rings (mathematics)
Semigroups
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Summary: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.
ISSN:2331-8422