Prof. T.T. Moh, on his page on the Jacobian Conjecture, mentions that

"the classical Jacobian criteria for power series, implies that $k[[f(x,y),g(x,y) ]]=k[[x,y]]$. Thus we have $$x=F(f,g), y=G(f,g)$$ as power series. "

What is meant by the Jacobian Criteria for Power Series? Is there a good exposition of this?

  • 1
    $\begingroup$ For two power series $f,g$ as above (or more generally, $n$ power series in $n$ variables), Jacobian criterion means the Jacobian $J(f,g)$ (the determinant in some books, where they think of $J$ as a square matrix) is a unit, then the above equality of rings holds. This is more or less the content of implicit/inverse function theorem. $\endgroup$
    – Mohan
    Oct 20, 2016 at 14:29


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