Vol. 36, No. 1, 1971

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The structure of serial rings

David Eisenbud and Phillip Alan Griffith

Vol. 36 (1971), No. 1, 109–121

A serial ring (generalized uniserial in the terminology of Nakayama) 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.

Mathematical Subject Classification
Primary: 16A48
Received: 3 March 1970
Published: 1 January 1971
David Eisenbud
University of California, Berkeley
970 Evans Hall
Berkeley CA 94720-3840
United States
Phillip Alan Griffith
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana IL 61801-2975
United States