Some Algorithms of Corner-Elements in Monomial Ideals

Abstract

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.