| Full text | |
| Author(s): |
Total Authors: 2
|
| Affiliation: | [1] Univ Sheffield, Dept Pure Math, Hicks Bldg, Sheffield, S Yorkshire - England
[2] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | COMMUNICATIONS IN ALGEBRA; v. 47, n. 10 MAR 2019. |
| Web of Science Citations: | 0 |
| Abstract | |
Let R be a ring (not necessarily with 1) and G be a finite group of automorphisms of R. The set of primes p such that and R is not p-torsion free, is called the set of bad primes. When the ring is -torsion free, i.e. the properties of the rings R and R-G are closely connected. The aim of the article is to show that this is also true when under natural conditions on bad primes. In particular, it is shown that the Jacobson radical (respectively, the prime radical) of the ring R-G is equal to the intersection of the Jacobson radical (respectively, 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-G and udim (R-G) <= udim(R) <= vertical bar G vertical bar udim(R-G) (AU) | |
| FAPESP's process: | 14/09310-5 - Algebraic structures and their representations |
| Grantee: | Vyacheslav Futorny |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 17/02946-0 - Polynomial integro-differential operators and their representations |
| Grantee: | Vyacheslav Futorny |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |