On Algebraically Maximal Valued Fields and Defectless Extensions
Canadian mathematical bulletin, Tome 55 (2012) no. 2, pp. 233-241

Voir la notice de l'article provenant de la source Cambridge University Press

Let $v$ be a Henselian Krull valuation of a field $K$ . In this paper, the authors give some necessary and sufficient conditions for a finite simple extension of $(K,\,v)$ to be defectless. Various characterizations of algebraically maximal valued fields are also given which lead to a new proof of a result proved by Yu. L. Ershov.
DOI : 10.4153/CMB-2011-148-0
Mots-clés : 12J10, 12J25, valued fields, non-Archimedean valued fields
Bishnoi, Anuj; Khanduja, Sudesh K. On Algebraically Maximal Valued Fields and Defectless Extensions. Canadian mathematical bulletin, Tome 55 (2012) no. 2, pp. 233-241. doi: 10.4153/CMB-2011-148-0
@article{10_4153_CMB_2011_148_0,
     author = {Bishnoi, Anuj and Khanduja, Sudesh K.},
     title = {On {Algebraically} {Maximal} {Valued} {Fields} and {Defectless} {Extensions}},
     journal = {Canadian mathematical bulletin},
     pages = {233--241},
     year = {2012},
     volume = {55},
     number = {2},
     doi = {10.4153/CMB-2011-148-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-148-0/}
}
TY  - JOUR
AU  - Bishnoi, Anuj
AU  - Khanduja, Sudesh K.
TI  - On Algebraically Maximal Valued Fields and Defectless Extensions
JO  - Canadian mathematical bulletin
PY  - 2012
SP  - 233
EP  - 241
VL  - 55
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-148-0/
DO  - 10.4153/CMB-2011-148-0
ID  - 10_4153_CMB_2011_148_0
ER  - 
%0 Journal Article
%A Bishnoi, Anuj
%A Khanduja, Sudesh K.
%T On Algebraically Maximal Valued Fields and Defectless Extensions
%J Canadian mathematical bulletin
%D 2012
%P 233-241
%V 55
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-148-0/
%R 10.4153/CMB-2011-148-0
%F 10_4153_CMB_2011_148_0

[1] [1] Aghigh, K. and Khanduja, S. K., On the main invariant of elements algebraic over a Henselian valued field. Proc. Edinb. Math. Soc. 45(2002), no. 1, 219–227. Google Scholar

[2] [2] Aghigh, K. and Khanduja, S. K., On chains associated with elements algebraic over a Henselian valued field. Algebra Colloq. 12(2005), no. 4, 607–616. Google Scholar

[3] [3] Endler, O., Valuation theory. Springer-Verlag, New York, 1972. Google Scholar

[4] [4] Engler, A. J. and Prestel, A., Valued fields. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2005. Google Scholar

[5] [5] Ershov, Yu. L., Multi-valued fields. Kluwer Academic, New York, 2001. Google Scholar

[6] [6] Popescu, N. and Zaharescu, A., On the structure of the irreducible polynomials over local fields. J. Number Theory 52(1995), no. 1, 98–118. Google Scholar | DOI

[7] [7] Ribenboim, P., Equivalent forms of Hensel's lemma. Exposition. Math. 3(1985), no. 1, 3–24. Google Scholar

[8] [8] Singh, A. P. and Khanduja, S. K., On a theorem of Tignol for defectless extensions and its converse. J. Algebra 288(2005), no. 2, 400–408. Google Scholar | DOI

Cité par Sources :