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arXiv · 1711.09080

Intrinsic valuation entropy

Luigi Salce·Simone Virili
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Abstract

We extend the notion of intrinsic entropy for endomorphisms of Abelian groups to endomorphisms of modules over an Archimedean non-discrete valuation domain $R$, using the natural non-discrete length function introduced by Northcott and Reufel for such a category of modules. We prove that this notion of entropy is a length function for the category of $R[X]$-modules, it satisfies (a suitably adapted version of) the Intrinsic Algebraic Yuzvinski Formula and that it is essentially the unique invariant for $Mod(R[X])$ with these properties.

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Luigi Salce, Simone Virili. 2017-11-24. Intrinsic valuation entropy. https://arxiv.org/abs/1711.09080

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