Quasi-socle ideals in Gorenstein numerical semigroup rings
| Autor: | Goto, Shiro, Kimura, Satoru, Matsuoka, Naoyuki |
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| Rok vydání: | 2007 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Quasi-socle ideals, that is the ideals $I$ of the form $I= Q : \mathfrak{m}^q$ in Gorenstein numerical semigroup rings over fields are explored, where $Q$ is a parameter ideal, and $\mathfrak{m}$ is the maximal ideal in the base local ring, and $q \geq 1$ is an integer. The problems of when $I$ is integral over $Q$ and of when the associated graded ring $\mathrm{G}(I) = \bigoplus_{n \geq 0}I^n/I^{n+1}$ of $I$ is Cohen-Macaulay are studied. The problems are rather wild; examples are given. Comment: 20 pages, to appear in Journal of Algebra |
| Databáze: | arXiv |
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