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

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  • Najib Mahdou

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.

Suggested Citation

  • Najib Mahdou, 2006. "On n -flat modules and n -Von Neumann regular rings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-6, October.
    • Handle: RePEc:hin:jijmms:090868
    DOI: 10.1155/IJMMS/2006/90868
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