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Totally Integrally Closed Azumaya Algebras

Published online by Cambridge University Press:  20 November 2018

R. Macoosh  and
R. Raphael
R. Macoosh
Affiliation:
Department of Mathematics Concordia University, Loyola Campus 7141 Sherbrooke St. W., Montreal, Quebec H4B 1R6
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Abstract

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Enochs introduced and studied totally integrally closed rings in the class of commutative rings. This article studies the same question for Azumaya algebras, a study made possible by Atterton's notion of integral extensions for non-commutative rings.

The main results are that Azumaya algebras are totally integrally closed precisely when their centres are, and that an Azumaya algebra over a commutative semiprime ring has a tight integral extension that is totally integrally closed. Atterton's integrality differs from that often studied but is very natural in the context of Azumaya algebras. Examples show that the results do not carry over to free normalizing or excellent extensions.

Keywords

16A16
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 4 , 01 December 1990 , pp. 398 - 403
Copyright
Copyright © Canadian Mathematical Society 1990

References

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