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More noneuclidian $ {\rm PID}$'s and Dedekind domains with prescribed class group


Authors: Paul Eakin and W. Heinzer
Journal: Proc. Amer. Math. Soc. 40 (1973), 66-68
MSC: Primary 13D15
DOI: https://doi.org/10.1090/S0002-9939-1973-0319975-8
MathSciNet review: 0319975
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Abstract: Let $ Z$ denote the integers, $ Q$ the rationals, $ X$ an indeterminate and $ G$ a finitely generated abelian group. Then there is a Dedekind domain $ D$ such that $ Z[X] \subset D \varsubsetneqq Q[X]$, and $ D$ has class group $ G$. If $ G = 0$ then $ D$ is a noneuclidian PID.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0319975-8
Keywords: Dedekind domain, euclidian ring, principal ideal domain, class group, Krull ring
Article copyright: © Copyright 1973 American Mathematical Society

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