Abstract
All rings considered in this paper will be associative with an identity element and all modules will be unitary. In Section 1 we shall consider some questions concerning the representation of a flat module as a directed union of flat submodules with a prescribed number of generators, in particular give a partial solution of the problem of determining those rings for which any flat module is a directed union of finitely generated projective submodules. In Section 2 we shall consider some questions about the weak dimension of power series rings over von Neumann regular rings.
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