Conditions for semiperfect ring to be a serial ring

Abstract

A ring R is called a semiperfect if R/J is a semisimple ring and any idempotent can be lifted following the modulo J with J = rad(R). A ring R is called a serial if R is a direct sum of uniserial submodules. This paper, I would like to propose some examples to distinguish the above-mentioned two-class rings and clarify the results of the fact that the class of semiperfect rings is a generalization of the class of serial rings in the document [1] and [5]. Moreover, we would also like to verify some of the conditions for the semiperfect ring to be the right serial ring (or left).

Keywords: Semiperfect rings, serial rings