关于非交换Noether环的二个定理

TWO THEOREMS ON NON-COMMUTATIVE NOETHERIAN RINGS

本文的第一部分包含了ＪＣＭｃＣｏｎｎｅｌ〔３〕中的定理的证明，其结果描述了一个非交换的Ｎｏｅｔｈｅｒ环，当每个理想都有一个生成元的正规集合的情形下素理想的符号幂的形式，且略去了〔３〕中定理的其它条件。第二部分包含了一个通常感兴趣的结果。如果右Ｎｏｅｔｈｅｒ环Ｒ有一个右商环Ｑ，且Ｉ是Ｒ的任意双侧理想，那么ＩＱ是Ｑ的一个双侧理想。

The first part of this paper contains a proof of a theorem of J.C.McConnell 3 .The result describes the form of the symbolic powers of a prime ideal of a non-comutative Noetherian ring,in the case when each ideal has a normalising set of generators.The result proved here is in fact stronger,since other conditions are omitted. \ \ The second part contains a result of more general interest.If a right Noetherian ring R has a right quotient ring Q and I is any two-sided ideal in R,then IQ is a two-sided ideal of Q.The result generalizes Theorem 1.16 of 2 .