arXiv subjects

Alexandr V. Mikhalev

Publications and source records attributed to Alexandr V. Mikhalev.

2 recordsLinked to original sources

arXiv2006

Elementary equivalence of the semigroup of invertible matrices with nonnegative elements

In this paper, we prove that the semigroups of invertible matrices with nonnegative elements over linearly oredered associative rings are elementarily equivalent if and only if the matrices have the same dimension and the rings are elementarily equivalent as ordered rings.

math.RA↗

arXiv2006

Automorphisms of the semigroup of invertible matrices with nonnegative elements

In this paper we prove that every automorphism of the semigroup of invertible matrices with nonnegative elements over a linearly oredered associative ring on some specially defined subgroup concides with the composition of an inner automorphism of the semigroup, an automorphism of the ring preserving the order, and a central homothety.

math.RA↗