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arXiv · 2609.00820

Krasner Completions of Filtered Bands

Toshiro Hiranouchi
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Abstract

We introduce the Krasner completion of a band equipped with a decreasing filtration by subgroups of its unit group and give a criterion for reconstruction from its quotient bands. We recover the Krasner--Linzi inverse-limit theorem for valued fields. We also obtain a valuation ring analogue of the Krasner--Linzi theorem and compare Krasner completions of unit bands with adic completion.

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Toshiro Hiranouchi. 2026-09-01. Krasner Completions of Filtered Bands. https://arxiv.org/abs/2609.00820

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