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研究生： 陳怡如
Chen Yi-Ju
論文名稱： 高斯多項式的容度
The content of Gaussian polynomials
指導教授： 劉容真
Liu, Jung-Chen
學位類別： 碩士
Master
系所名稱： 數學系
Department of Mathematics
論文出版年： 2001
畢業學年度： 89
語文別： 英文
論文頁數： 58
中文關鍵詞： 高斯多項式 、content ideal 、Gorenstein 、approximately Gorenstein 、Gasuuain for polynomials of degree at most n 、Hilbert function 、reduction
英文關鍵詞： Gaussian polynomial, content ideal, Gorenstein, approximately Gorenstein, Gasuuain for polynomials of degree at most n, Hilbert function, reduction
論文種類： 學術論文
相關次數： 點閱：212  下載：3 
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    • 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.

    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.

    INTRODUCTION CHAPTER 1 Gaussian Plynomials §1 Some Properties of Gaussian Polynomials §2 Review of Properties of Gorenstein Rings and Approximately Gorenstein Rings §3 Gaussian and Gorenstein CHAPTER 2 Gaussian for Polynomials of Degree At Most n §1 Gaussian for Polynomials of Degree At Most n §2 Gaussian Polynomials Over Locally Noetherian Rings CHAPTER 3 Another View of Gaussian Polynomials §1 Hilbert functions §2 Prime Characteristic §3 Characteristic Zero REFERENCES

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    [HH] W. Heinzer and C. Huneke, {it Gaussian polynomials and content ideals}, Proc. Amer. Math. Soc. {

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    [M] H. Matsumura, {it Commtative ring theory}, Cambridge University Press, 1986

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