It is proved that if <mml:math alttext="$R$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>R</mml:mi></mml:math> is a semiprime ELT-ring and every simple right <mml:math alttext="$R$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>R</mml:mi></mml:math>-module is flat then <mml:math alttext="$R$" id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>R</mml:mi></mml:math> is regular. Is <mml:math alttext="$R$" id="E4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>R</mml:mi></mml:math> regular if <mml:math alttext="$R$" id="E5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>R</mml:mi></mml:math> is a semiprime ELT-ring and every simple right <mml:math alttext="$R$" id="E6" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>R</mml:mi></mml:math>-module is flat? In this note, we give a positive answer to the question.

International Journal of Mathematics and Mathematical Sciences

Semiprime SF-rings whose essential left ideals are two-sided

Abstract

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