Quasi-socle ideals in local rings with Gorenstein tangent cones

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dc.creatorGoto, Shiro
dc.creatorKimura, Satou
dc.creatorMatsuoka, Naoyuki
dc.creatorPhuong, Tran Thi
dc.date2007-10-06
dc.date2008-07-29
dc.date.accessioned2026-07-07T09:53:03Z
dc.date.available2026-07-07T09:53:03Z
dc.descriptionQuasi-socle ideals, that is the ideals $I$ of the form $I= Q : \mathfrak{m}^q$ in a Noetherian local ring $(A, \mathfrak{m})$ with the Gorenstein tangent cone $\mathrm{G}(\mathfrak{m}) = \bigoplus_{n \geq 0}{\mathfrak{m}}^n/{\mathfrak{m}}^{n+1}$ are explored, where $q \geq 1$ is an integer and $Q$ is a parameter ideal of $A$ generated by monomials of a system $x_1, x_2, ..., x_d$ of elements in $A$ such that $(x_1, x_2, ..., x_d)$ is a reduction of $\mathfrak{m}$. The questions of when $I$ is integral over $Q$ and of when the graded rings $\mathrm{G}(I) = \bigoplus_{n \geq 0}I^n/I^{n+1}$ and $\mathrm{F}(I) = \bigoplus_{n \ge 0}I^n/\mathfrak{m} I^n$ are Cohen-Macaulay are answered. Criteria for $\mathrm{G} (I)$ and $\mathcal{R} (I) = \bigoplus_{n \geq 0}I^n$ to be Gorenstein rings are given.
dc.description16 pages, to appear in Journal of Commutative Algebra
dc.identifierhttps://arxiv.org/abs/0710.1387
dc.identifierhttp://arxiv.org/abs/0710.1387
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/165814
dc.subjectCommutative Algebra
dc.subject13H10, 13A30, 13B22, 13H15
dc.titleQuasi-socle ideals in local rings with Gorenstein tangent cones
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