关于分式理想的值集
On value sets of fractional ideals
摘要：
本文研究了容许环中分式理想关于固定理想的对偶性，并研究了容许环中对偶理想对的值集之间的关系。容许环是一类包含代数曲线在奇点处的局部环的环。我们刻画了典型理想的对称关系的长度之间的某些从属关系的关联理想的一对对偶理想。特别地，我们将对偶分式理想对的值集中的绝对极大值和相对极大值之间的对称性推广到其它类型的极大点。我们的结果推广和补充了其他作者以前的结果。
英文摘要：
The aim of this work is to study duality of fractional ideals with respect to a fixed ideal and to investigate the relationship between value sets of pairs of dual ideals in admissible rings, a class of rings that contains the local rings of algebraic curves at singular points. We characterize canonical ideals by means of a symmetry relation between lengths of certain quotients of associated ideals to a pair of dual ideals. In particular, we extend the symmetry among absolute and relative maximals in the sets of values of pairs of dual fractional ideals to other kinds of maximal points. Our results generalize and complement previous ones by other authors.
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