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

Abstract

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

To appear in Journal of Algebra and its Applications