Quasi-socle ideals in Gorenstein numerical semigroup rings

Details Quasi-socle ideals in Gorenstein numerical semigroup rings Quasi-socle ideals in Gorenstein numerical semigroup rings

2007-10-06

arxiv.org/abs/0710.1386v2

Mathematics

Commutative Algebra

20 pages, to appear in Journal of Algebra

Scientific paper

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.

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