Bavula, V. and Futorny, V. (2019) Rings of invariants of finite groups when the bad primes exist. Communications in Algebra, 47 (10). 4114-4124 . ISSN 0092-7872
Abstract
Let R be a ring (not necessarily with 1) and G be a finite group of automorphisms of R. The set B(R, G) of primes p such that p | |G| and R is not p-torsion free, is called the set of bad primes. When the ring is |G|-torsion free, i.e., B(R, G) is empty set, the properties of the rings R and R^G are closely connected. The aim of the paper is to show that this is also true when B(R, G) is not empty set under natural conditions on bad primes. In particular, it is shown that the Jacobson radical (resp., the prime radical) of the ring R^G is equal to the intersection of the Jacobson radical (resp., the prime radical) of R with R^G; if the ring R is semiprime then so is R^G; if the trace of the ring R is nilpotent then the ring itself is nilpotent; if R is a semiprime ring then R is left Goldie iff the ring R^G is so, and in this case, the ring of G-invariants of the left quotient ring of R is isomorphic to the left quotient ring of R^G and \udim (R^G)\leq \udim (R)\leq |G| \udim (R^G).
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 Taylor & Francis Group, LLC. This is an author-produced version of a paper subsequently published in Communications in Algebra. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Bad primes; group of automorphisms; nilpotent ideal; semiprime ring; semisimple Artinian ring; the Jacobson radical; the prime radical; the ring of invariants |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 01 Dec 2017 15:52 |
Last Modified: | 29 Jul 2020 15:18 |
Status: | Published |
Publisher: | Taylor & Francis |
Refereed: | Yes |
Identification Number: | 10.1080/00927872.2019.1579336 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:124655 |