关于受限制的弱准素环的一点注记

A Note on Restricted Weakly Primary Rings

中文摘要:

      交换环R称为(受限制的)弱准素环,如果R中的每个(非零)主理想都是准素理想.本文证明了一个没有单位元的交换环R是受限制的弱准素环当且仅当R是每个元素都是幂零元的交换环或者R是仅含一个真素理想P的没有单位元的交换环并且P不真包含R的任何非零理想.

英文摘要:

      In this paper, we show that a commutative ring R without identity is a restricted weakly primary ring if and only if R is a ring in which each element is nilpotent or a ring without identity in which there is the unique proper prime ideal P and P does not properly contain any non-zero ideal of R.