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Lifting Ideals in Noncommutative Integral Extensions

Published online by Cambridge University Press:  20 November 2018

K. Hoechsmann
K. Hoechsmann*
Affiliation:
University of British Columbia, Vancouver, British Columbia
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This note is intended as a commentary on a part of the paper [1] by Gulliksen, Ribenboim, and Viswanathan. It takes its inspiration from a colloquium talk by P. Ribenboim.

Our aim is a partial generalization of the theorem of Cohen-Seidenberg (cf. [2], IX. 1, Propositions 9 and 10) to noncommutative algebras.

Definition. Let A be a ring with 1 in the center of another ring B (with the same 1). B is said to be integral over A, if each element b ∊ B satisfies an integral equation

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 1 , March 1970 , pp. 129 - 130
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Gulliksen, T., Ribenboim, P., Viswanathan, T. M., An elementary note on group rings, (to appear).Google Scholar
2. Lang, S., Algebra, Addison-Wesley, Reading, Mass. (1965).Google Scholar