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Proceedings of the American Mathematical Society

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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
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.

References [Enhancements On Off] (What's this?)

  • [AEH] Shreeram S. Abhyankar, William Heinzer, and Paul Eakin, On the uniqueness of the coefficient ring in a polynomial ring, J. Algebra 23 (1972), 310–342. MR 0306173
  • [C] Luther Claborn, Every abelian group is a class group, Pacific J. Math. 18 (1966), 219–222. MR 0195889
  • [B] N. Bourbaki, Éléments de mathématique. Fasc. XXXI. Algèbre commutative. Chap. 7, Actualités Sci. Indust., no. 1314, Hermann, Paris, 1965. MR 41 #5339.
  • [S$ _{1}$] Pierre Samuel, About Euclidean rings, J. Algebra 19 (1971), 282–301. MR 0280470
  • [S$ _{2}$] P. Samuel, Lectures on unique factorization domains, Notes by M. Pavman Murthy. Tata Institute of Fundamental Research Lectures on Mathematics, No. 30, Tata Institute of Fundamental Research, Bombay, 1964. MR 0214579

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Keywords: Dedekind domain, euclidian ring, principal ideal domain, class group, Krull ring
Article copyright: © Copyright 1973 American Mathematical Society