  Let $\mathbb{K}$ be an algebraically closed field of characteristic zero and
let $\mathbb{K}_{C}[[x_{1},...,x_{e}]]$ be the ring of formal power series in
several variables with exponents in a line free cone $C$. We consider
irreducible polynomials
$f=y^n+a_1(\underline{x})y^{n-1}+\ldots+a_n(\underline{x})$ in
$\mathbb{K}_{C}[[x_{1},...,x_{e}]][y]$ whose roots are in
$\mathbb{K}_{C}[[x_{1}^{\frac{1}{n}},...,x_{e}^{\frac{1}{n}}]]$. We generalize
to these polynomials the theory of Abhyankar-Moh. In particular we associate
with any such polynomial its set of characteristic exponents and its semigroup
of values. We also prove that the set of values can be obtained using the set
of approximate roots. We finally prove that polynomials of ${\mathbb
K}[[\underline{x}]][y]$ fit in the above set for a specific line free cone (see
Section 4).
