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Inertial subalgebras of algebras possessing finite automorphism groups

Part of: Local rings and semilocal rings

Published online by Cambridge University Press:  09 April 2009

Nicholas S. Ford
Nicholas S. Ford
Affiliation:
The Fayette Campus The Pennsylvania State UniversityUniontown, Pennsylvania 15401, USA
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Abstract

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Let R be a commutative ring with identity, and let A be a finitely generated R-algebra with Jacobson radical N and center C. An R-inertial subalgebra of A is a R-separable subalgebra B with the property that B+N=A. Suppose A is separable over C and possesses a finite group G of R-automorphisms whose restriction to C is faithful with fixed ring R. If R is an inertial subalgebra of C, necessary and sufficient conditions for the existence of an R-inertial subalgebra of A are found when the order of G is a unit in R. Under these conditions, an R-inertial subalgebra B of A is characterized as being the fixed subring of a group of R-automorphisms of A. Moreover, A ⋍ B ⊗R C. Analogous results are obtained when C has an R-inertial subalgebra S ⊃ R.

MSC classification

Secondary: 13H99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 3 , November 1979 , pp. 335 - 345
Copyright
Copyright © Australian Mathematical Society 1979

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