Abstract
To any integral algebra with valuation an abelian group is associated, which measures how much the uniqueness of the division with remainder is violated. The analogy with the divisor class group is discussed. Examples of such groups are computed in cases of formal local rings of some cusps on an algebraic curve.
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The author was partially supported by the KBN grant 2P03A 050 22.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Maszczyk, T. Division with remainder in algebras with valuation. Monatsh Math 164, 183–199 (2011). https://doi.org/10.1007/s00605-010-0233-9
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DOI: https://doi.org/10.1007/s00605-010-0233-9