Some Results On The Fixed Ring

Given a subgroup of Aut(R), we have a skew group ring RG={Σg∈Grgg\rg∈R} by gr=rg-1,while there are a finite number of rg≠0; one also can construct a subring of R, called fixed ring RG={r|rg=r,(?)g∈G}. In the second part of this article, we have studied the inner and outer automorphism in the maximal quotient ring, after which had been researched in the two-side ring of quotient by Kharchenko. At last, we talked about the relationship of global dimension among ring R, skew group ring RG and fixed ring RG after Martin Lorenz.Introduction, to introduce the background and the main results of this disserta-tion.Chapter one, to introduce some commonly used concepts and some common results.Chapter two is devoted to investigate the inner and outer automorphism in the maximal quotient ring.Chapter three is devoted to use the morita context to investigate the relationship of global dimension among ring R, skew group ring RG and fixed ring RG.