Rings of invariants of finite groups when the bad primes exist

Autor(es)

Bavula, Volodymyr ^[1] ; Futorny, Vyacheslav ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sheffield, Dept Pure Math, Hicks Bldg, Sheffield, S Yorkshire - England

^[2] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: COMMUNICATIONS IN ALGEBRA; v. 47, n. 10 MAR 2019.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 14/09310-5 - Estruturas algébricas e suas representações
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 17/02946-0 - Operadores polinomial íntegro-diferenciais e suas representações
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional