Automorphisms of the semigroup of invertible matrices with nonnegative elements over commutative partially ordered rings
E. I. Bunina, P. P. Semenov
TL;DR
This paper characterizes automorphisms of the semigroup of nonnegative invertible matrices over commutative partially ordered rings containing the rationals, extending previous results to a broader class of rings.
Contribution
It provides a description of automorphisms of G_n(R) for commutative partially ordered rings containing Q, generalizing earlier work on linearly ordered rings.
Findings
Automorphisms are characterized for G_n(R) over these rings.
Results extend previous classifications to broader ring structures.
The work applies for matrices of size n>2.
Abstract
Suppose that R is an ordered ring, G_n(R) is a subsemigroup of , 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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Taxonomy
TopicsAdvanced Topics in Algebra · Finite Group Theory Research · Rings, Modules, and Algebras