On canonical bases of a formal ${\mathbb K}-algebra

We study canonical bases of a subalgebra ${\bf A}={\mathbb K}[![f_1,\dots,f_s]!]\subseteq {\mathbb K}[![x_1,\dots,x_n]!]$overafield${\mathbb K}$,andweassociatewith${\bf A}$ a fan called the canonical fan of $\mathbf{A}$. This generalizes the notion of the standard fan of an ideal.