Abstract
In §1 we give a formula for the inverse of a formal power series map F over a commutative ℚ-algebra R satisfying det J F(0) ∈ R*. More precisely, for each integer d ≥ 1 this formula computes the homogeneous component of degree d of the formal inverse of F. The very simple proof is an immediate consequence of Taylor’s formula. Using the well-known bound for the degree of the inverse of a polynomial automorphism over a reduced ring, we obtain an invertibility criterion for a polynomial map over such a ring.
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© 2000 Springer Basel AG
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van den Essen, A. (2000). Invertibility criteria and inversion formulae. In: Polynomial Automorphisms. Progress in Mathematics, vol 190. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8440-2_3
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DOI: https://doi.org/10.1007/978-3-0348-8440-2_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9567-5
Online ISBN: 978-3-0348-8440-2
eBook Packages: Springer Book Archive