On the product of vector spaces in a commutative field extension

Shalom Eliahou, Michel Kervaire, Cédric Lecouvey

Let $K\subset L$ be a commutative field extension. Given $K$-subspaces $A,B$ of $L$, we consider the subspace $<AB>$ spanned by the product set $AB=\{ab\mid a\in A,b\in B\}$.…