A study of irreducible polynomials over henselian valued fields via distinguished pairs

2014 ◽  
pp. 1-10
Author(s):  
Kamal Aghigh ◽  
Anuj Bishnoi ◽  
Sudesh Khanduja ◽  
Sanjeev Kumar
Keyword(s):  
Irreducible Polynomials ◽  
Valued Fields ◽  
Henselian Valued Fields

Model Theory of Henselian Valued Fields

1989 ◽  
pp. v-vi
Author(s):  
H.-D. Ebbinghaus ◽  
J. Fernandez-Prida ◽  
M. Garrido ◽  
D. Lascar ◽  
M. Rodriquez Artalejo
Keyword(s):  
Model Theory ◽  
Valued Fields ◽  
Henselian Valued Fields

scholarly journals HENSELIAN VALUED FIELDS AND inp-MINIMALITY

2019 ◽  
Vol 84 (4) ◽  
pp. 1510-1526
Author(s):  
ARTEM CHERNIKOV ◽  
PIERRE SIMON
Keyword(s):  
Type Result ◽  
Valued Fields ◽  
Henselian Valued Fields

AbstractWe prove that every ultraproduct of p-adics is inp-minimal (i.e., of burden 1). More generally, we prove an Ax-Kochen type result on preservation of inp-minimality for Henselian valued fields of equicharacteristic 0 in the RV language.

On factorization of polynomials in henselian valued fields

2018 ◽  
Vol 46 (7) ◽  
pp. 3205-3221 ◽  
Author(s):  
Anuj Jakhar ◽  
Sudesh K. Khanduja ◽  
Neeraj Sangwan
Keyword(s):  
Valued Fields ◽  
Henselian Valued Fields ◽  
Factorization Of Polynomials

scholarly journals Uniformly defining valuation rings in Henselian valued fields with finite or pseudo-finite residue fields

2013 ◽  
Vol 164 (12) ◽  
pp. 1236-1246 ◽  
Author(s):  
Raf Cluckers ◽  
Jamshid Derakhshan ◽  
Eva Leenknegt ◽  
Angus Macintyre
Keyword(s):  
Valued Fields ◽  
Valuation Rings ◽  
Henselian Valued Fields ◽  
Residue Fields

Onpth Roots in Henselian Valued Fields

2007 ◽  
Vol 35 (2) ◽  
pp. 435-442
Author(s):  
Saurabh Bhatia ◽  
Sudesh K. Khanduja
Keyword(s):  
Valued Fields ◽  
Henselian Valued Fields

On finite intersections of ?henselian valued? fields

1985 ◽  
Vol 52 (1-3) ◽  
pp. 37-61 ◽  
Author(s):  
Bernhard Heinemann
Keyword(s):  
Valued Fields ◽  
Henselian Valued Fields

scholarly journals ON THE MAIN INVARIANT OF ELEMENTS ALGEBRAIC OVER A HENSELIAN VALUED FIELD

2002 ◽  
Vol 45 (1) ◽  
pp. 219-227 ◽  
Author(s):  
Kamal Aghigh ◽  
Sudesh K. Khanduja
Keyword(s):  
Upper Bound ◽  
Algebraic Closure ◽  
Subject Classification ◽  
Unique Extension ◽  
Valued Fields ◽  
Valued Field ◽  
Henselian Valued Fields ◽  
Alpha Beta ◽  
Henselian Valuation

AbstractLet $v$ be a henselian valuation of a field $K$ with value group $G$, let $\bar{v}$ be the (unique) extension of $v$ to a fixed algebraic closure $\bar{K}$ of $K$ and let $(\tilde{K},\tilde{v})$ be a completion of $(K,v)$. For $\alpha\in\bar{K}\setminus K$, let $M(\alpha,K)$ denote the set $\{\bar{v}(\alpha-\beta):\beta\in\bar{K},\ [K(\beta):K] \lt [K(\alpha):K]\}$. It is known that $M(\alpha,K)$ has an upper bound in $\bar{G}$ if and only if $[K(\alpha):K]=[\tilde{K}(\alpha):\tilde{K}]$, and that the supremum of $M(\alpha,K)$, which is denoted by $\delta_{K}(\alpha)$ (usually referred to as the main invariant of $\alpha$), satisfies a principle similar to the Krasner principle. Moreover, each complete discrete rank 1 valued field $(K,v)$ has the property that $\delta_{K}(\alpha)\in M(\alpha,K)$ for every $\alpha\in\bar{K}\setminus K$. In this paper the authors give a characterization of all those henselian valued fields $(K,v)$ which have the property mentioned above.AMS 2000 Mathematics subject classification: Primary 12J10; 12J25; 13A18

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