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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Commutative monoid rings as Hilbert rings


Author: Robert Gilmer
Journal: Proc. Amer. Math. Soc. 94 (1985), 15-18
MSC: Primary 13B25; Secondary 20M25
DOI: https://doi.org/10.1090/S0002-9939-1985-0781046-2
MathSciNet review: 781046
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Abstract: Let $S$ be a cancellative monoid with quotient group of torsion-free rank $\alpha$. We show that the monoid ring $R(S)$ is a Hilbert ring if and only if the polynomial ring $R[{\{ {X_i}\} _{i \in I}}]$ is a Hilbert ring, where $\left | I \right | = \alpha$.


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Keywords: Monoid ring, group ring, Hilbert ring, <IMG WIDTH="22" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img7.gif" ALT="$G$">-ideal, <IMG WIDTH="22" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$G$">-domain, pseudoradical
Article copyright: © Copyright 1985 American Mathematical Society