Abstract
The first three sections of this chapter investigate derivations in the case B has one or more nice divisorial properties, in addition to the ongoing assumption that B is a commutative k-domain, where k is a field of characteristic zero. Subsequent sections discuss quasi-extensions, G-critical elements, the degree of a derivation, trees and cables, exponential automorphisms, construction of kernel elements by transvectants and Wronskians, and recognition of polynomial rings.
To understand a ring, study its LNDs. To understand an LND, study its kernel. To understand a kernel, study its LNDs.
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Notes
- 1.
This property is what the authors term strong invariance.
- 2.
The condition f and g are not both constant is missing from Davenport’s original formulation, but is necessary for the result to be valid.
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Freudenburg, G. (2017). Further Properties of LNDs. In: Algebraic Theory of Locally Nilpotent Derivations. Encyclopaedia of Mathematical Sciences, vol 136.3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55350-3_2
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