内自同构作用下的不变元

The Invariant Elements Under Inner Automorphic Actions

设R是半完备环,R的内自同构群为G,本文证明了若对任意0≠e=e^2∈R,1+e是R中的可逆元,则R在G作用下的不变元是R的中心.

Suppose R is a semiperfect ring, and tis inner automorphic group is G. In this paper, it is shown that if 1+ e is invertible in R for all 0 ≠ e = e2 ∈ R, then the invariant subring of R under inner automorphic actions agrees with the center of R.