Extension of Endomorphisms of the Subsemigroup GE 2 + (R) to Endomorphisms of GE 2 + (R[x]), Where R is a Partially-Ordered Commutative Ring Without Zero Divisors

Abstract

Let R be a partially ordered commutative ring without zero divisors, Gn(R) be the subsemigroup of GLn(R) consisting of matrices with nonnegative elements, and GE + n (R) be its subsemigroup generated by elementary transformation matrices, diagonal matrices, and permutation matrices. In this paper, we describe in which cases endomorphisms of GE + 2 (R) can be extended to endomorphisms of GE + 2 (R[x]).