Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
157 tokens/sec
GPT-4o
8 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Rings of invariants of finite groups when the bad primes exist (1704.07190v1)

Published 24 Apr 2017 in math.RA

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 RG 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 RG is equal to the intersection of the Jacobson radical (resp., the prime radical) of R with RG; if the ring R is semiprime then so is RG; 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 RG 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 RG and \udim (RG)\leq \udim (R)\leq |G| \udim (RG).

Summary

We haven't generated a summary for this paper yet.