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研究生: 呂又寧
Yo-Ning Lu
論文名稱: 對於單項式理想Q,(Q:X)諸貌
Some Aspects of (Q:X) for Monomial Ideals Q
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: 2007
畢業學年度: 95
語文別: 英文
論文頁數: 70
中文關鍵詞: 單項式理想最小單項式生成集角落元素
英文關鍵詞: monomial ideal, minimal monomial generating set, corner-element
論文種類: 學術論文
相關次數: 點閱:156下載:15
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  • 對於多項式環k[X1,X2,…,Xd]上的單項式理想Q,我們探討 (Q:X) 的最小單項式生成集,其中X=(X1,X2,…,Xd)為k[X1,X2,…,Xd]中的最大單項式理想。此外,我們進一步研究當s足夠大時,(Q:Xs) 為何。

    For the monomial ideals Q in the polynomial ring k[X1,X2,…,Xd] over a field k, we discuss the minimal monomial generating set of (Q:X), where X=(X1,X2,…,Xd) is the maximal monomial ideal of k[X1,X2,…,Xd]. Moreover, we study (Q:Xs) when s is big enough.

    1.Introduction........................2 2.Preliminaries.......................4 3.Minimal Generating Set of (Q:X).....9 4.(Q:X^n).............................43 5.A Viewpoint from Graph Theory.......55

    G. Agnarsson, The Number of Outside Corners of Monomial Ideals,Journal of Pure and Applied Algebra 117&118 (1997), 3–21.

    M.F. Atyiah and I.G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, 1969.

    D. Cox, J. Little, and D. O’Shea, Ideals, Varieties, and Algorithms,Springer-Verlag, 1992.

    W. Heinzer, M. Ahmad, L.J. Ratliff, Jr., and K. Shah, Parametric Decompositions of Monomial Ideals(II), Journal of Algebra, 187(1997), 120–149.

    N. Hartsfield and G. Ringel, Pearls in Graph Theory: A Comprehensive Introduction, Academic Press, Inc., 1990.

    W. Heinzer, L.J. Ratliff, Jr., and K. Shah, Parametric Decompositions of Monomial Ideals(I), Houston Journal of Mathematics, 21(1)(1995), 29–52.

    J.-C. Liu, Algorithms on Parametric Decomposition of Monomial Ideals, Communications in Algebra, 30(7) (2002), 3435–3456.

    E. Miller and B. Sturmfels, Combinatorial Commutative Algebra, Graduate Texts in Mathemetics, vol. 227, Springer-Verlag, 2004.

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