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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| Published in | arXiv.org |
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| Main Author | |
| Format | Paper |
| Language | English |
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Ithaca
Cornell University Library, arXiv.org
29.08.2024
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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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| AbstractList | 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. |
| Author | Endo, Naoki |
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| Snippet | 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... |
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| Title | How many ideals whose quotient rings are Gorenstein exist? |
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