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arXiv · 2305.08697

Applications of Generalized Universal Valuations

William Bernardoni
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Abstract

We introduce a generalization of the universal valuation semiring defined by Jeffrey and Noah Giansiracusa. We then explicitly characterize the additive structure of this semiring and show that, when applied to $\mathbb Q$, this characterization gives the Non-Archimedean case of Ostrowski's theorem. We conclude with examples of non-commutative valuations and their applications, such as the detection of the existence of representations of rings in ultrametric vector spaces.

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William Bernardoni. 2023-05-15. Applications of Generalized Universal Valuations. https://arxiv.org/abs/2305.08697

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