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The structure of serial
rings
David Eisenbud and Phillip Alan Griffith |
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Vol. 36 (1971), No. 1, 109–121
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Abstract |
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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
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Milestones
Received: 3 March 1970
Published: 1 January 1971
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Authors |
| David Eisenbud | |
| Mathematics University of California, Berkeley 970 Evans Hall Berkeley CA 94720-3840 United States |
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| Phillip Alan Griffith | |
| Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana IL 61801-2975 United States |
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| http://www.math.uiuc.edu/People/griffith.html | |
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