Revisiting Kneser’s Theorem for Field Extensions

A Theorem of Hou, Leung and Xiang generalised Kneser’s addition Theorem to field extensions. This theorem was known to be valid only in separable extensions, and it was a conjecture of Hou that it should be valid for all extensions. We give an alternative proof of the theorem that also holds in the...

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Bibliographic Details
Published in:Combinatorica (Budapest. 1981) Vol. 38; no. 4; pp. 759 - 777
Main Authors: Bachoc, Christine, Serra, Oriol, Zémor, Gilles
Format: Journal Article Publication
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2018
Springer
Springer Nature B.V
Springer Verlag
Subjects:
11 Number theory
11P Additive number theory; partitions
12 Field theory and polynomials
12F Field extensions
Addition theorem
Additive combinatorics
Classificació AMS
Combinatorial analysis
Combinatorics
Field theory (Physics)
linear versions
Matemàtiques i estadística
Mathematics
Mathematics and Statistics
Particions (Matemàtica)
Partitions (Mathematics)
Rings and Algebras
Teoria de camps (física)
Teoria de cossos i polinomis
Teoria de nombres
Theorems
Àlgebra
Àrees temàtiques de la UPC
11P70
11T99
12F99
ISSN:0209-9683, 1439-6912
Online Access:Get full text
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Summary:A Theorem of Hou, Leung and Xiang generalised Kneser’s addition Theorem to field extensions. This theorem was known to be valid only in separable extensions, and it was a conjecture of Hou that it should be valid for all extensions. We give an alternative proof of the theorem that also holds in the non-separable case, thus solving Hou’s conjecture. This result is a consequence of a strengthening of Hou et al.’s theorem that is inspired by an addition theorem of Balandraud and is obtained by combinatorial methods transposed and adapted to the extension field setting.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:0209-9683
1439-6912
DOI:10.1007/s00493-016-3529-0