|
|||||
|
|
Kahl bewertete Ringe in der nichtarchimedischen Analysis |
|
| Authors: | Ulrich Güntzer Reinhold Remmert |
| Institution: | (1) II. Mathematisches Institut der FU, Königin-Luise-Str. 24-26, D-1000 Berlin 33;(2) Math. Institut der Universität, Roxelerstr. 64, D-4400 Münster |
| Abstract: | An integral domain R provided with a non-archimedean valuation | | is called  bald (kahl), if there exists a real number  , 0<<1, such that the value set |R|   does not meet the open interval (, 1). Bald rings are important in non-archimedean analysis because the method of iteration (classical and well known for fields with discrete valuation) is convergent in these rings. In this note it is shown that each valuated field contains big bald subrings, more precisely:Let K be a completely valuated field and let
denote the valuation ring. Let {a } 1 be a sequence in
converging to zero. Then the smallest complete local subring of
containing all a is bald.Herrn Karl Stein zum 60. Geburtstag gewidmet |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |