This article is cited in 11 papers

On rings with a discrete divisor class group

V. I. Danilov


Abstract: We consider the conjecture: $C(A)=C(A[[T]])$ for a local ring $A$ if and only if the divisor class group of the strict henselization $C(^\mathrm{sh}A)$ has a finite number of generators. This conjecture is proved in two cases: 1) $A$ has characteristic $0$, 2) $A$ is an equicharacteristic ring of an isolated singularity.
Bibliography: 15 titles.

UDC: 513 015.7

MSC: Primary 13J15, 13F15; Secondary 14L15

Received: 07.04.1971

 English version: Mathematics of the USSR-Sbornik, 1972, 17:2, 228–236

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