关于伪准素环的注记

A Note on Pseudo Primary Rings

英文关键词:primary ideal  commutative ring.

中文摘要:

      一个有单位元的交换环Ｒ称为伪准素环，如果Ｒ的每个非零理想都是某个准素理想之幂．本文证明了环Ｒ是伪准素环当且仅当Ｒ是准素环或Ｒ是两个域的直和或Ｒ是至多具有三个素理想的一维局部环，并且每个非零理想或是某个极小素理想之幂或是某个属于极大理想的准不比理想之幂.

英文摘要:

      A commutative ring with identity R is called a pseudo primary ring if eachnon-zero ideal of R is a power of a primary ideal. In this note we prove that a ring Ris a pseudo primary ring if and only if R is a primary ring or R is a direct sum of twofields or R is a one-dimensional local ring with at most three prime ideals in which eachnon-zero ideal is a power of a minimal prime ideal or is a power of some primary idealbelonging to the maximal ideal.