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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{hiranouchi2026krasner,
  title = {{Krasner Completions of Filtered Bands}},
  author = {Toshiro Hiranouchi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00820},
  eprint = {2609.00820},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00820},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Krasner Completions of Filtered Bands
AU  - Toshiro Hiranouchi
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00820
UR  - https://arxiv.org/abs/2609.00820
AB  - 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.
ER  -