Let $R$ be a semiprime ring with $U_{\trm{s}}$ its maximal symmetric ring of quotients and let $\rho_1$ and $\rho_2$ be two right ideals of $R$. We show that $\ell_R(\rho_1)=\ell_R(\rho_2)$ if and only if $\rho_1$ and $\rho_2$ satisfy the same differential identities with coefficients in $U_{\trm{s}}$, where $\ell_R(\rho_i)$ denotes the left annihilator of $\rho_i$ in $R$. This gives a generalization of several previous results in this area.

AMS 2000 Mathematics subject classification: Primary 6R50. Secondary 16N60