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Galois Theory for Rings with Finitely Many Idempotents

Published online by Cambridge University Press:  22 January 2016

O. E. Villamayor  and
D. Zelinsky
O. E. Villamayor
Affiliation:
Universidad de Buenos Aires, Northwestern University
D. Zelinsky
Affiliation:
Universidad de Buenos Aires, Northwestern University
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In [5], Chase, Harrison and Rosenberg proved the Fundamental Theorem of Galois Theory for commutative ring extensions S ⊃ R under two hypotheses: (i) 5 (and hence R) has no idempotents except 0 and l; and (ii) 5 is Galois over R with respect to a finite group G—which in the presence of (i) is equivalent to (ii′): S is separable as an R-algebra, finitely generated and projective as an R-module, and the fixed ring under the group of all R-algebra automorphisms of S is exactly R.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 2 , July 1966 , pp. 721 - 731
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

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