关于凝聚局部环的正则性

On the Regularity of Coherent Local Rings

本文证明了极大理想m是有限生成的交换凝聚局部环（R，M）是正则的充分必要条件是m可以由一个正则R-序列生成，推广了文献[1]中相应的结论并给出了一个由正则凝聚局部环构造大量的非正则凝聚局部环的方法．

In this paper, it is proved that a commutative coherent local ring with maximal ideal m, which is finitely generated, is regular if and only if m can be generated by a regular R-sequence. Some corresponding results in [1] are generalized, and a method for constructing non-regular coherent local rings from regular coherent local rings is gived.