How many ideals whose quotient rings are Gorenstein exist?
Fuente:
arXiv
Guardado en:
| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917762062876672 |
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| author | Endo, Naoki |
| author_facet | Endo, Naoki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_19633 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | How many ideals whose quotient rings are Gorenstein exist? Endo, Naoki Commutative Algebra 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. |
| title | How many ideals whose quotient rings are Gorenstein exist? |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2305.19633 |