Hostname: page-component-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-16T16:47:41.810Z Has data issue: false hasContentIssue false
  • English
  • Français

On Algebraically Maximal Valued Fields and Defectless Extensions

Published online by Cambridge University Press:  20 November 2018

Anuj Bishnoi  and
Sudesh K. Khanduja
Anuj Bishnoi
Affiliation:
Department of Mathematics, Panjab University, Chandigarh 160014, Indiae-mail: anuj.bshn@gmail.com; skhand@pu.ac.in
Sudesh K. Khanduja
Affiliation:
Department of Mathematics, Panjab University, Chandigarh 160014, Indiae-mail: anuj.bshn@gmail.com; skhand@pu.ac.in
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

12J1012J25valued fieldsnon-Archimedean valued fields
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 2 , 01 June 2012 , pp. 233 - 241
Copyright
Copyright © Canadian Mathematical Society 2012

References

[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] 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] Endler, O., Valuation theory. Springer-Verlag, New York, 1972.Google Scholar
[4] Engler, A. J. and Prestel, A., Valued fields. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2005.Google Scholar
[5] Ershov, Yu. L., Multi-valued fields. Kluwer Academic, New York, 2001.Google Scholar
[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. http://dx.doi.org/10.1006/jnth.1995.1058 Google Scholar
[7] Ribenboim, P., Equivalent forms of Hensel's lemma. Exposition. Math. 3(1985), no. 1, 3–24.Google Scholar
[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. http://dx.doi.org/10.1016/j.jalgebra.2005.02.016 Google Scholar