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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Krull and global dimensions of semiprime Noetherian PI-rings

Authors: Richard Resco, Lance W. Small and J. T. Stafford
Journal: Trans. Amer. Math. Soc. 274 (1982), 285-295
MSC: Primary 16A33; Secondary 16A38
MathSciNet review: 670932
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Abstract: In this paper it is shown that if $ R$ is a semiprime Noetherian PI-ring of finite global dimension, then the Krull dimension of $ R$ is less than or equal to its global dimension. The proof depends upon two preliminary results on arbitrary Noetherian PI-rings, which are of independent interest: (i) any height two prime ideal of $ R$ contains infinitely many height one prime ideals; (ii) the localization of the polynomial ring $ R[x]$ at its set of monic elements is a Jacobson ring.

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Keywords: Noetherian PI-rings, Krull dimension, global dimension, Jacobson rings
Article copyright: © Copyright 1982 American Mathematical Society