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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Dedekind domains and graded rings


Authors: Fabien Decruyenaere and Eric Jespers
Journal: Proc. Amer. Math. Soc. 110 (1990), 21-26
MSC: Primary 13F05; Secondary 13G05, 16A03
MathSciNet review: 1027092
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Abstract: We prove that a Dedekind domain $ R$, graded by a nontrivial torsionfree abelian group, is either a twisted group ring $ {k^t}[G]$ or a polynomial ring $ k[X]$, where $ k$ is a field and $ G$ is an abelian torsionfree rank one group. It follows that $ R$ is a Dedekind domain if and only if $ R$ is a principal ideal domain. We also investigate the case when $ R$ is graded by an arbitrary nontrivial torsionfree monoid.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1027092-7
PII: S 0002-9939(1990)1027092-7
Article copyright: © Copyright 1990 American Mathematical Society