In this paper, we introduce and study the class of flat modules which are generalizations of both flat modules and -flat modules. The weak global dimension w.gl.dim of a commutative ring is also introduced and studied. We show that, for a ring ,w.gl.dim if and only if-if and only if is a von Neumann ring. It is also proved that, for a strongly ring , w.gl.dim if and only if each nonnil ideal of is flat, if and only if is a , if and only if is a .
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