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Serial Right Noetherian Rings

Published online by Cambridge University Press:  20 November 2018

Surjeet Singh
Surjeet Singh*
Affiliation:
Kuwait University, Kuwait
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A module M is called a serial module if the family of its submodules is linearly ordered under inclusion. A ring R is said to be serial if RR as well as RR are finite direct sums of serial modules. Nakayama [8] started the study of artinian serial rings, and he called them generalized uniserial rings. Murase [5, 6, 7] proved a number of structure theorems on generalized uniserial rings, and he described most of them in terms of quasi-matrix rings over division rings. Warfield [12] studied serial both sided noetherian rings, and showed that any such indecomposable ring is either artinian or prime. He further showed that a both sided noetherian prime serial ring is an (R:J)-block upper triangular matrix ring, where R is a discrete valuation ring with Jacobson radical J. In this paper we determine the structure of serial right noetherian rings (Theorem 2.11).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 36 , Issue 1 , 01 February 1984 , pp. 22 - 37
Copyright
Copyright © Canadian Mathematical Society 1984

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