- 學位論文
Some Algorithms of Corner-Elements in Monomial Ideals
Some Algorithms of Corner-Elements in Monomial Ideals
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摘要
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。
並列摘要
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.
並列關鍵字
無資料參考文獻
[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.