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研究生： 李麗梅
LI-MEI LI
論文名稱： Some Algorithms of Corner-Elements in Monomial Ideals
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： 42
英文關鍵詞： monomial ideal, corner-element, algorithm
論文種類： 學術論文
相關次數： 點閱：224  下載：7 
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    • Monomial ideals 在某些數學領域是重要的。在 [HRS], [HMRS] and [L] 這三篇論文中，corner-elements 在找唯一的 irredundant parametric decomposition of a monomial ideal上扮演一個重要的角色。雖然在幾篇論文裡已經有一些找corner-elements 的演算法，但是使用這些演算法去找 I-corner-elements，我們必需先計算I的irredundant parametric decomposition 或者是不在 I 的the monomials。因此我們給了兩種不用先計算它們就可以找到corner-elements 的方法。最後，我們在 k[X,Y,Z] 裡造一些具有某些特殊性質的 monomial ideals。

    Monomial ideals are important in several areas of mathematics. In [HRS], [HMRS] and [L], corner-elements play an important role in finding the unique irredundant parametric decomposition of a monomial ideal. There are a few algorithms for finding corner-elements provided in several articles, however, using these algorithms to find
    I-corner-elements, we need to compute the irredundant parametric decomposition of I or the monomials not in I first. Hence we give two methods to find corner-elements without computing them. Finally, we construct some monomial ideals in k[X,Y,Z] having some special property.

    1 Introduction 1 2 Preliminaries 4 2.1 Irredundant Parametric Decomposition 2.2 An Algorithm for Finding Corner-Elements 3 Algorithms for Finding Corner-Elements 11 3.1 An Equivalent Condition Related to Corner-Elements 3.2 One Method to Find Corner-Elements 3.3 Another Method to Find Corner-Elements 4 Some Relations of The Numbers of Generators of I and I–Corner–Elements 29 4.1 A case where I has no corner-elements 4.2 Some Special Cases

    [L] J.-C. Liu, Algorithms on Parametric Decomposition of Monomial Ideals, Comm. in Algebra, 30(7)(2002), 3435-3456.

    [CLO] D. Cox, J. Little, and D. O’shea, Ideals, Varieties, and Algorithms : An Introduction to Computational Algebraic Geometry and Commutative Algebra, 2nd ed., Springer-Verlag, New York-Berlin-Heidelberg, 1997.

    [HMRS] W. Heinzer, Ahmad Mirbagheri, L. J. Ratliff, Jr., and K. Shah, Parametric Decompositions of Monomial Ideals(II), J. Alegbra 187(1997), 120-149.

    [HRS] W. Heinzer, L. J. Ratliff, Jr., and K. Shah, Parametric Decompositions of Monomial Ideals(I), Houston J. Math 21(1)(1995), 29-52.

    [EH] J. A. Eagon and M. Hochster, R-sequences and Indeterminates, Quart. J. Math 25(1974), 61-71.

    [T] D. Taylor, Ideals Generated By Monomials In An R-Sequence, Ph.D. Dissertation, U. Chicago, 1966.

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