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LEFT ANNIHILATORS CHARACTERIZED BY DIFFERENTIAL IDENTITIES

Published online by Cambridge University Press:  01 July 2004

Tsiu-Kwen Lee  and
Ching-Yueh Pan
Tsiu-Kwen Lee
Affiliation:
Department of Mathematics, National Taiwan University, Taipei 106, Taiwan (tklee@math.ntu.edu.tw; cypan@math.ntu.edu.tw)
Ching-Yueh Pan
Affiliation:
Department of Mathematics, National Taiwan University, Taipei 106, Taiwan (tklee@math.ntu.edu.tw; cypan@math.ntu.edu.tw)
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Abstract

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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

Keywords

semiprime ringmaximal ring of quotientsgeneralized polynomial identities (GPIs)differential identity
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 47 , Issue 2 , June 2004 , pp. 411 - 419
Copyright
Copyright © Edinburgh Mathematical Society 2004