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\(S\)-units and \(S\)-class group in algebraic function fields. (English) Zbl 0265.12003

Es seien \(k\) ein Körper, \(k[x]\) der Polynomring über \(k\), \(K\) eine endliche separable Erweiterung des Körpers \(k(x)\) und \(R\) der ganze Abschluß von \(k[x]\) in \(K\). In dieser Arbeit werden die Einheitengruppe und die Klassengruppe von \(R\) untersucht.

MSC:

11R58 Arithmetic theory of algebraic function fields
11R27 Units and factorization
11R29 Class numbers, class groups, discriminants
14H05 Algebraic functions and function fields in algebraic geometry
14G25 Global ground fields in algebraic geometry
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References:

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