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Rings With Finite Maximal Invariant Subrings

Published online by Cambridge University Press:  20 November 2018

Charles Lanski
Charles Lanski*
Affiliation:
Department of Mathematics University of Southern California Los Angeles, CA 90089-1113 U.S.A. email: e-mail: clanski@mtha.usc.edu
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Abstract

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We prove that if φ is an (anti-) automorphism of a ring R with finite orbits on R, or integral over the integers, and if R contains a finite maximal φ-invariant subring, then R must be finite. Special cases are when φ has finite order or is an involution. Two corollaries are that R must be finite when R contains only finitely many φ-invariant subrings or has both ascending and descending chain conditions on φ invariant subrings. These generalize results in the literature for the special case when φ = idR.

Keywords

16P1016W2016P70
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 3 , 01 June 1996 , pp. 596 - 606
Copyright
Copyright © Canadian Mathematical Society 1996

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