Abstract

AbstractWe prove that if φ is an (anti-) automorphism of a ringRwith finite orbits onR, or integral over the integers, and ifRcontains a finite maximal φ-invariant subring, thenRmust be finite. Special cases are when φ has finite order or is an involution. Two corollaries are thatRmust be finite whenRcontains 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.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.