A characterization of prime Noetherian P. I. rings and a theorem of MoriNagata
Author:
Amiram Braun
Journal:
Proc. Amer. Math. Soc. 74 (1979), 915
MSC:
Primary 16A38
MathSciNet review:
521864
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Abstract: Let R be a noetherian prime p.i. ring, C the center of R and its normalization. It is proved that R is integral over its center iff is a Krull domain. We also give a simple proof for the following theorem [7]: The normalization of a commutative noetherian domain is Krull.
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 D. Eisenbud, Subrings of Artinian and Noetherian rings, Math. Ann. 185 (1970), 247249. MR 0262275 (41:6885)
 [2]
 E. Formanek, Noetherian P. I. rings, Comm. Algebra 1 (1974), 7986. MR 0357489 (50:9957)
 [3]
 A. V. Jategaonkar, Principal ideal theorem for Noetherian P.I. rings, J. Algebra 35 (1975), 1722. MR 0371944 (51:8161)
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 W. Heinzer, J. Ohm and R. L. Pendleton, On integral domains of the form , p minimal, J. Reine Angew. Math. 241 (1970), 147159. MR 0263793 (41:8393)
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 I. Kaplansky, Commutative rings, Allyn and Bacon, Boston, Mass., 1970. MR 0254021 (40:7234)
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 Jacob R. Matijevic, Maximal ideal transform of Noetherian rings, Proc. Amer. Math. Soc. 54 (1976), 4952. MR 0387269 (52:8112)
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 M. Nagata, Local rings, Interscience, New York, 1962. MR 0155856 (27:5790)
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 J. Nishimura, Note on integral closures of a Noetherian integral domain, J. Math. Kyoto Univ. 16 (1976), 117122. MR 0409433 (53:13188)
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 C. Procesi, Rings with polynomial identity, Dekker, New York, 1973. MR 0366968 (51:3214)
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 W. Schelter, On the KrullAkizuki theorem, J. London Math. Soc. 13 (1976), 263264. MR 0404329 (53:8131)
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 , Integral extensions of rings satisfying a polynomial identity, J. Algebra 40 (1976), 245257. MR 0417238 (54:5295)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197905218646
PII:
S 00029939(1979)05218646
Article copyright:
© Copyright 1979
American Mathematical Society
