Finite Principal Ideal Rings

Abstract

This paper determines the structure of finite rings whose two sided ideals are principal as left ideals, and as right ideals. Such rings will be called principal ideal rings. Although finite rings have been studied extensively [1], [5], [12], [14] and the tools necessary for describing finite principal ideal rings have been available for thirty years, these structure theorems (which are essentially given in a more general setting in [4]) seem to have been overlooked. In particular, let or be an endomorphism of a ring V.