Orthogonal Left Derivations of Semi-Prime Rings

Abstract

In this paper we show a few outcomes concerning two remaining deductions on a semi-prime ring are displayed. These outcomes are identified with an outcome which is motivated by Posner's hypothesis. This outcome affirms that if R is a 2-torsion free semi-prime ring, δ and g are non-zero remaining inductions of R with the end goal that g is a surjective on R, and g(y)δ(x)=g(x)δ(y) for all x,y∈R. At that point δ g can't be a non-zero left derivation. A thought of orthogonal left derivations emerges here.