IJPAM: Volume 56, No. 1 (2009)


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 $R$ with char $R\neq 2$ and $2R=R$ have been defined and studied. Necessary conditions for an S-strong Jordan ideal of $R$ have been obtained. It has been proved that if $J$ is an S-strong Jordon ideal of $R, S$ is the set of symmetric elements of $R$ and $B_J$ is the set associated with $J$, 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 $R$ into an associative ring $A$ 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 $x \in R$, $k \in K$, $(\phi(x^2)-(\phi(x))^2)\phi(k)=\phi(k)(\phi(x^{*^2})-(\phi(x^*))^2)$.

Received: August 2, 2009

AMS Subject Classification: 16A66, 16A72

Key Words and Phrases: ideals, Jordan ideal, S-strong Jordan ideal

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 56
Issue: 1