The structure of serial rings

Abstract

A serial ring (generalized uniserial in the terminology of Nakayanta) is one whose left and right free modules are direct sums of modules with unique finite composition series (uniserial modules.) This paper presents a module-theoretic discussion of the structure of serial rings, and some onesided characterizations of certain kinds of serial rings. As an application of the structure theory, an easy proof is given of A. W. Goldie’s characterization of serial rings with trivial singular ideal. © 1971, Pacific Journal of Mathematics.