高斯多項式的容度

The content of Gaussian polynomials

陳怡如(Chen Yi-Ju)

指導教授 ： 劉容真

國立臺灣師範大學/理學院/數學系/碩士(2000年)

摘要

Abstract
We consider the question: over an integral domain, is the content ideal of a nonzero Gaussian polynomial an invertible ideal? In this thesis, we discuss two different approaches to study this question. First, we discuss this question over approximately Gorenstein rings. We show that over a Noetherian domain, the content ideal of a Gaussian polynomial is invertible. Next, We make use of Hilbert polynomials to discuss this question. We show that over an integrally closed Noetherian local domain, a Gaussian polynomial has an invertible content ideal.

關鍵字

高斯多項式 ； content ideal ； Gorenstein ； approximately Gorenstein ； Gasuuain for polynomials of degree at most n ； Hilbert function ； reduction

並列摘要

Abstract
We consider the question: over an integral domain, is the content ideal of a nonzero Gaussian polynomial an invertible ideal? In this thesis, we discuss two different approaches to study this question. First, we discuss this question over approximately Gorenstein rings. We show that over a Noetherian domain, the content ideal of a Gaussian polynomial is invertible. Next, We make use of Hilbert polynomials to discuss this question. We show that over an integrally closed Noetherian local domain, a Gaussian polynomial has an invertible content ideal.

並列關鍵字

Gaussian polynomial ； content ideal ； Gorenstein ； approximately Gorenstein ； Gasuuain for polynomials of degree at most n ； Hilbert function ； reduction

參考文獻

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