Bulletin of the
Korean Mathematical Society BKMS

It is proved that $k[X_1,\dots,X_v]$ localized at the ideal $(X_1,\dots$, $X_v)$, where $k$ is a field and $X_1,\dots,X_v$ indeterminates, is not weakly quasi-complete for $v\ge2$, thus proving a conjecture of D. D. Anderson and solving a problem from ``Open Problems in Commutative Ring Theory'' by Cahen, Fontana, Frisch, and Glaz.

Keywords: quasi-completeness, Noetherian ring, commutative ring, polynomial ring, localization, ring of formal power series, completion

MSC numbers: 13A15, 13B30, 13B35, 13E05, 16P40, 16P50, 16S85