This article is cited in 24 papers

On a conjecture of Samuel

V. I. Danilov


Abstract: We construct examples disproving Samuel's conjecture stating that the ring $A[[T]]$ is factorial for a complete factorial local ring $A$. We also prove a theorem asserting (under some restrictions) that the ring $A[[T]]$ is factorial for a “'geometrically” factorial ring $A$.
Bibliography: 16 titles.

UDC: 513.015.7

MSC: 13F15, 13D03, 13H05, 51A10, 20J06

Received: 09.05.1969

 English version: Mathematics of the USSR-Sbornik, 1970, 10:1, 127–137

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