IJPAM: Volume 56, No. 1 (2009)

ON S-STRONG JORDAN IDEALS

Anita Verma
Department of Mathematics
University of Delhi
Delhi, 110 007, INDIA
e-mail: [email protected]

Abstract.S-strong Jordan ideals of a semi-prime ring with char $R\neq 2$ and have been defined and studied. Necessary conditions for an S-strong Jordan ideal of have been obtained. It has been proved that if is an S-strong Jordon ideal of is the set of symmetric elements of and is the set associated with , then $SB_J \subseteq B_J$ and for all $u \in J$ , $u^2 \in B_J$ . Finally, as an application, we prove that if $\phi$ is a non-zero additive mapping of into an associative ring such that $\phi(ab+b^* a^*) =\phi(a)\phi(b)+\phi(b^*)\phi(a^*)$ , $a, b \in R$ , then $\Ker \phi \cap S=(0)$ and for all $x \in R$ , $k \in K$ , $(\phi(x^2)-(\phi(x))^2)\phi(k)=\phi(k)(\phi(x^{*^2})-(\phi(x^*))^2)$ .