A commutative ring R is called a (restricted) (p)-ring if each (nonzero) principal ideal of R is power of a prime ideal. S. Singh and R. Kumar in [1] pointed out that to classify restricted (p)-rings without identity ...A commutative ring R is called a (restricted) (p)-ring if each (nonzero) principal ideal of R is power of a prime ideal. S. Singh and R. Kumar in [1] pointed out that to classify restricted (p)-rings without identity in terms of other well-known types of rings remains open. In this note we solve this problem by elementary methods and some techniques.展开更多
文摘A commutative ring R is called a (restricted) (p)-ring if each (nonzero) principal ideal of R is power of a prime ideal. S. Singh and R. Kumar in [1] pointed out that to classify restricted (p)-rings without identity in terms of other well-known types of rings remains open. In this note we solve this problem by elementary methods and some techniques.
