Strong shift equivalence of 2 by 2 nonnegative integral matrices

Abstract

It is known that if A and B are nontriangular 2 by 2 nonnegative integral matrices similar over the integers and -tr A $\leq$ det A, then A and B are strongly shift equivalent. Suppose that A and B are nonnegative 2 by 2 integral matrices similar over the integers. In the article it is shown that if -2 tr A $\leq$ $\det A < -tr A $ and if $\mid {\det A}\mid$ is not a prime, then A and B are strong shift equivalent.