 If "R" is local, any finitely presented flat module is free of finite rank, thus projective.Despite being defined in terms of homological algebra, flatness has profound geometric implications.For example, if an "R"-algebra "S" is flat, the dimensions of the fibers
(for prime ideals "p" in "R") have the "expected" dimension, namely dim "S" − dim "R" + dim ("R" / "p").