Geodesic
Locally unbounded topological fields with topological nilpotents
J. E. Marcos1
1 Departamento Algebra y Geometría Facultad de Ciencias 47005 Valladolid, Spain
Fundamenta Mathematicae, Tome 173 (2002) no. 1, pp. 21-32

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We construct some locally unbounded topological fields having topologically nilpotent elements; this answers a question of Heine. The underlying fields are subfields of fields of formal power series. In particular, we get a locally unbounded topological field for which the set of topologically nilpotent elements is an open additive subgroup. We also exhibit a complete locally unbounded topological field which is a topological extension of the field of $p$-adic numbers; this topological field is a missing example in the classification of complete first countable fields given by Mutylin.
DOI : 10.4064/fm173-1-2
Keywords: construct locally unbounded topological fields having topologically nilpotent elements answers question heine underlying fields subfields fields formal power series particular get locally unbounded topological field which set topologically nilpotent elements additive subgroup exhibit complete locally unbounded topological field which topological extension field p adic numbers topological field missing example classification complete first countable fields given mutylin

J. E. Marcos 1

1 Departamento Algebra y Geometría Facultad de Ciencias 47005 Valladolid, Spain 
@article{10_4064_fm173_1_2,
     author = {J. E. Marcos},
     title = {Locally unbounded topological fields
 with topological nilpotents},
     journal = {Fundamenta Mathematicae},
     pages = {21--32},
     publisher = {mathdoc},
     volume = {173},
     number = {1},
     year = {2002},
     doi = {10.4064/fm173-1-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm173-1-2/}
}
TY  - JOUR
AU  - J. E. Marcos
TI  - Locally unbounded topological fields
 with topological nilpotents
JO  - Fundamenta Mathematicae
PY  - 2002
SP  - 21
EP  - 32
VL  - 173
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm173-1-2/
DO  - 10.4064/fm173-1-2
LA  - en
ID  - 10_4064_fm173_1_2
ER  - 
%0 Journal Article
%A J. E. Marcos
%T Locally unbounded topological fields
 with topological nilpotents
%J Fundamenta Mathematicae
%D 2002
%P 21-32
%V 173
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm173-1-2/
%R 10.4064/fm173-1-2
%G en
%F 10_4064_fm173_1_2
J. E. Marcos. Locally unbounded topological fields
 with topological nilpotents. Fundamenta Mathematicae, Tome 173 (2002) no. 1, pp. 21-32. doi: 10.4064/fm173-1-2

Cité par Sources :