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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| Vydané v: | Combinatorica (Budapest. 1981) Ročník 38; číslo 4; s. 759 - 777 |
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| Jazyk: | English |
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Springer Berlin Heidelberg
01.08.2018
Springer Springer Nature B.V Springer Verlag |
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| ISSN: | 0209-9683, 1439-6912 |
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| Abstract | 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. |
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| AbstractList | 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. 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. Peer Reviewed |
| Audience | Academic |
| Author | Bachoc, Christine Serra, Oriol Zémor, Gilles |
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| SubjectTerms | 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 |
| Title | Revisiting Kneser’s Theorem for Field Extensions |
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