On Invertible Bimodules and Automorphisms of Noncommutative Rings

Abstract

In this article, we attempt to generalize the result that for a commutative ring $R$ the outer automorphism group of $R$-automorphisms of ${M_n}(R)$ is abelian of exponent $n$. It is shown that a slightly weaker stable version of the result is still valid for affine semiprime noetherian pi rings. We also show that the automorphism group of an affine commutative domain of positive dimension acts faithfully on the spectrum of the domain. We investigate other questions involving bimodules and automorphisms and extend a result of Smith on the first Weyl algebra as a fixed ring.