The structure of some right Noetherian rings with Krull dimension one
Author:
C. L. Wangneo
Journal:
Proc. Amer. Math. Soc. 118 (1993), 677680
MSC:
Primary 16P40; Secondary 16P20, 16P60
MathSciNet review:
1127145
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Abstract: In this note we prove a structure theorem for a right Noetherian ring with krull dimension one having a right Artinian quotient ring and, moreover, that has a finitely generated, faithful, critical right module with krull dimension equal to one. We end this note with some examples that clarify certain features of this theorem.
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 K. A. Brown, T. H. Lenagan, and J. T. Stafford, Weak ideal invariance and localisation, J. London Math. Soc. (2) 21 (1980). MR 576183 (81i:16016)
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 A. W. Chatters and C. R. Hajarnavis, Rings with chain conditions, Pitman, London, 1980. MR 590045 (82k:16020)
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 R. Gordon, Primary decomposition in right noetherian rings, Comm. Algebra (1974), 491524. MR 0360691 (50:13138)
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 , Some aspects of noncommutative noetherian rings, Lecture Notes in Math., vol. 545, SpringerVerlag, New York, 1975, pp. 105127.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199311271451
PII:
S 00029939(1993)11271451
Article copyright:
© Copyright 1993
American Mathematical Society
