Monatshefte für Mathematik

, Volume 164, Issue 2, pp 183–199 | Cite as

Division with remainder in algebras with valuation

  • Tomasz MaszczykEmail author
Open Access


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.


Valuations Weierstrass Division Theorem Singularities 

Mathematics Subject Classification (2000)

13F30 13J10 14H20 


Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of WarsawWarszawaPoland

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