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A Remark about Noncommutative Integral Extensions

Published online by Cambridge University Press:  20 November 2018

A. G. Heinicke
A. G. Heinicke*
Affiliation:
University of Western Ontario, London, Ontario
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Let B be a ring with unity, A a imitai subring of the centre Cof B. Suppose further that B is A-integral. (That is, every element of B satisfies a monic polynomial with coefficients in A.) Under these assumptions, Hoechsmann [2] showed that "contraction to A" is a mapping from:

  1. (1) The prime ideals of B onto the prime ideals of A,

  2. (2) The maximal ideals of B onto the maximal ideals of A.

In this note we show that, under additional assumptions, a noncommutative version of the rest of the Cohen-Seidenberg "going up theorem" can be established.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 3 , September 1970 , pp. 359 - 361
Copyright
Copyright © Canadian Mathematical Society 1970

Footnotes

(1)

Supported by National Research Council.

References

1. Herstein, I. N., Noncommutative rings, Caru. Math. Monograph. 15, 1968.Google Scholar
2. Hoechsmann, K., Lifting ideals in noncommutative integral extensions, Canad. Math. Bull.(1) 13 (1970), 129-130.Google Scholar