• LEFT JORDAN AND LEFT DERIVATIONS ON SEMI PRIME RINGS

Abstract

In this paper first we prove that for 2-torsion semi prime ring R and let a, b ЄR , if for all x Є R the relation holds axb+bxa=0 holds then axb=bxa=0 is fulfilled for all x ЄR. Using this result we prove that ′:R→R be a Jordan derivation .In this case ′ is a derivation.

Key Words: Derivation of a Ring, Left Derivation of a Ring, Jordan Derivation of a ring, Left Jordan Derivation of a ring, Semiprime ring, Characteristic of a ring.