Styrt

pp. 17-27

 The problem under consideration is a generalized concept of a principal ideal ring and does not suggest that the ring does not have divisors of zero. The problem of classification of principal ideal rings in the new sense and their connection with principal ideal rings in the usual sense are investigated. It is proved that each principal ideal ring (maybe with divisors of zero) without nilpotent elements can be decomposed into a direct product of finitely many principal ideal rings without divisors of zero. For principal ideal rings with nilpotent elements the classification problem is not studied.