Positive derivations on lattice ordered rings of matrices

Abstract

Here we consider a commutative l-ring R with unit. We show that the only positive derivation on the l-ring Mn(R) is 0 if and only if the only positive derivation on R is zero. Also, if the only positive derivation on R is zero, we prove that for certain semiprime sub l-rings S of Mn(R) the only positive derivation on S is zero. Then, we study positive derivations on sub l-rings of Mn(R) where R is an Archimedean l-ring.

Quaestiones Mathematicae 30(2007), 275–284