For prime rings <mml:math alttext="$R$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>R</mml:mi></mml:math>, we characterize the set <mml:math alttext="$U \cap C_{R}([U,U])$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>U</mml:mi><mml:mo>&#8745;</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mi>R</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>U</mml:mi><mml:mo>,</mml:mo><mml:mi>U</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>,
where <mml:math alttext="$U$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>U</mml:mi></mml:math> is a right ideal of <mml:math alttext="$R$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>R</mml:mi></mml:math>; and we apply our result to
obtain a commutativity-or-finiteness theorem. We include extensions
to semiprime rings.

International Journal of Mathematics and Mathematical Sciences

A note on centralizers

Abstract

Copyright