It is known (see Reference 7, Corollary, p. 459) that any finitely-presented left (right) flat module is pro¬jective and any finitely-generated flat left module over a left-Noether an ring is projective. It will be shown in the presetit communication that any finitely-generated left A-flat module is A-projective, if and only if, for any n, the matrix ring A over A satisfies the boundary minimality or maximality conditions for the principal ideals.
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