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arXiv · 1510.01354

Revisiting Kneser's Theorem for Field Extensions

Christine Bachoc·Oriol Serra·Gilles Zémor
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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 a transposition to extension fields of an addition theorem of Balandraud.

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Christine Bachoc, Oriol Serra, Gilles Zémor. 2017-02-24. Revisiting Kneser's Theorem for Field Extensions. https://doi.org/10.1007/s00493-016-3529-0

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