Automorphisms of the semigroup of invertible matrices with nonnegative elements over commutative partially ordered rings

Abstract

Suppose that R is an ordered ring, G_n(R) is a subsemigroup of $G{L}_n(R)$, consisting of all matrices with nonnegative elements. A.V. Mikhalev and M.A. Shatalova described all automorphisms of G_n(R), where R is a linearly ordered skewfield and n>1. E.I. Bunina and A.V. Mikhalev found all automorphisms of G_n(R), if R is an arbitrary linearly ordered associative ring with 1/2, n>2. In this paper we describe automorphisms of G_n(R), if R is a commutative partially ordered ring, containing Q, n>2.

30 pages