An analogue of Vosper's theorem for extension fields
An analogue of Vosper's theorem for extension fields
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DOI：
10.1017/s0305004117000044
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发表时间：
2015-01
影响因子：
0.8
通讯作者：
C. Bachoc;O. Serra;G. Zémor
中科院分区：
文献类型：
--
作者：
C. Bachoc;O. Serra;G. Zémor
本文研究域扩张L/F中F-线性子空间对S，T的特征，使得S的元素与T的元素的乘积的线性跨距ST具有小维数。我们的中心结果是一个线性类似的Vozen定理，它给出了向量空间S，T在有限域F的素扩张L中的结构，对于有限域F，当dim FS，dim FT ≥ 2和dim FST ≥ [L：F] − 2时，\开始{linenomath}$$ \dim_FST =\dim_FS +\dim_FT T-1，$$\end{linenomath}。
Abstract We are interested in characterising pairs S, T of F-linear subspaces in a field extension L/F such that the linear span ST of the set of products of elements of S and of elements of T has small dimension. Our central result is a linear analogue of Vosper's Theorem, which gives the structure of vector spaces S, T in a prime extension L of a finite field F for which \begin{linenomath}$$ \dim_FST =\dim_F S+\dim_F T-1, $$\end{linenomath} when dim FS, dim FT ⩾ 2 and dim FST ⩽ [L : F] − 2.