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

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