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

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

2007-11-04

arxiv.org/abs/0711.0532v1

Mathematics

Rings and Algebras

30 pages

Scientific paper

Suppose that R is an ordered ring, G_n(R) is a subsemigroup of $GL_n(R)$, 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.

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