Büchi Sequences in Local Fields and Local Rings
Volume 58 / 2010
Bulletin Polish Acad. Sci. Math. 58 (2010), 109-115
MSC: Primary 11B83; Secondary 11Sxx.
DOI: 10.4064/ba58-2-2
Abstract
We prove that there exist infinite Büchi i sequences in some local rings and local fields, with the exception of the ring ${\mathbb Z}_p$ of $p$-adic integers. In ${\mathbb Z}_p$ there are only finite but arbitrarily long Büchi sequences.
