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generalized polynomial identities (gpis)

Proceedings of the Edinburgh Mathematical Society (1)

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LEFT ANNIHILATORS CHARACTERIZED BY DIFFERENTIAL IDENTITIES
Tsiu-Kwen Lee, Ching-Yueh Pan
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 47 / Issue 2 / June 2004

Published online by Cambridge University Press:

01 July 2004, pp. 411-419
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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