Let <mml:math alttext="$A$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>A</mml:mi></mml:math> be a ring and <mml:math alttext="$\Lambda$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#923;</mml:mi></mml:math> a finitely generated <mml:math alttext="$A$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>A</mml:mi></mml:math>-module.
We give necessary and sufficient conditions for projectivity and
flatness of a module over the endomorphism ring of <mml:math alttext="$\Lambda$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#923;</mml:mi></mml:math>.

International Journal of Mathematics and Mathematical Sciences

Projectivity and flatness over the endomorphism ring of a finitely generated module

Abstract

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