Division with remainder in algebras with valuation
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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.
KeywordsValuations Weierstrass Division Theorem Singularities
Mathematics Subject Classification (2000)13F30 13J10 14H20
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