臺灣博碩士論文加值系統

　　本篇論文主要在於討論特殊ㄧ維的Gorenstein local 環上的associated graded ring 會是Cohen-Macaulay 或 Gorenstein的情況

　In this thesis, we will discuss some conditions on one dimensional Gorenstein local ring so that the associated graded ring is either Cohen-Macaulay or Gorenstein.

Contents
1. Introduction 3
2. Preliminary 6
3. Main Theorem 12
4. Some Examples 24
References 27

References
[BH] W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge University Press,
1993.
[C] Yan-Hao Chen, On the Associated Graded Rings of Semigroup Rings, MS 2009.
[HUK] W. Heinzer, B. Ulrich and Mee-Kyoung Kim, The Gorenstein and Complete
Intersection Properties of Associated Graded rings, Journal of Pure and Applied
Algebra. Vol. 201, (2005), 264-283.
[K] E. Kunz, Introduction to Commutative Algebra and Algebraic Geometry,
Birkhauser Boston, 1985.
[M] H. Matsumura, Commutative Ring Theory, Cambridge University Press, 1986.
[S] J.J. Sylvester, Question 7382, Mathematical Questions with their Solutions, Ed-
ucational Times. Vol. 41 (1884), 21.
[VV] P. Valabrega and G. Valla, From Rings and Regular Sequences, Nagoya Math.
J. Vol. 72 (1978), 93-101.