On <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math>-flat modules and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math>-Von Neumann regular rings

Mahdou, Najib

doi:https://doi.org/10.1155/IJMMS/2006/90868

International Journal of Mathematics and Mathematical Sciences

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Volume 2006 | Article ID 090868 | https://doi.org/10.1155/IJMMS/2006/90868

On n-flat modules and n-Von Neumann regular rings

Najib Mahdou¹

Received04 May 2006

Revised20 Jun 2006

Accepted21 Aug 2006

Published29 Oct 2006

Abstract

We show that each R-module is n-flat (resp., weakly n-flat) if and only if R is an (n,n−1)-ring (resp., a weakly (n,n−1)-ring). We also give a new characterization of n-Von Neumann regular rings and a characterization of weak n-Von Neumann regular rings for (CH)-rings and for local rings. Finally, we show that in a class of principal rings and a class of local Gaussian rings, a weak n-Von Neumann regular ring is a (CH)-ring.

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Copyright

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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