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If such a set $ A$ of size $ m$ exists, all its admissible pairwise sums must lie in its complement, thus $ $ \binom{m}{2} \leq 2^n-m, $ $ which gives $ $ m\leq 2^{(n+1)/2}\qquad (1)$ $ . Since $ a+b=c$ is the same as $ a+b+c=0$ in characteristic 2, a randomly chosen set ofRead more

Let $ A\subset B$ be an injective homomorphism of noetherian integral domains s.t. $ B$ is finitely generated as $ A$ -module and $ A$ normal. Suppose that the normalization $ \bar B$ of $ B$ is finitely generated as $ A$ -module. And call $ F_A\subset F_B$ the induced extension of fraction fields. (i)Read more