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並前往https://www.ams.org/journals/proc/1985-094-01/S0002-9939-1985-0781046-2/S0002-9939-1985-0781046-2.pdf

COMMUTATIVE MONOID RINGS AS HILBERT RINGS

Let S be a cancellative monoid with quotient group of torsion-free rank a. We show that the monoid ring R[S] is a Hilbert ring if and only if the polynomial.

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