滤正则序列与局部上同调

摘要

More general definitions of regular sequence and depth in commutative algebra were given. And some characterizations of them were shown with the help of the techniques and knowledge of homo-logical algebra such as local cohomology, long exact sequences, and that of commutative algebra such as localization and associated primes ideals. Furthermore, properties of the supports of some extension groups and some local cohomology groups were shown.%对交换代数中正则序列和深度的概念进行了推广,并利用局部上同调、短正合列诱导长正合列等同调代数手段及伴随素理想、局部化等交换代数内容和方法对推广的深度给了一些刻画.进一步,利用以上技术手段,对一些扩张群及局部上同调群的支集进行了刻画并研究了其性质.