A characterization property on field equivalent to algebraicity on Banach spaces

Details A characterization property on field equivalent to algebraicity on Banach spaces A characterization property on field equivalent to algebraicity on Banach spaces

2007-06-28

arxiv.org/abs/0706.4181v1

Mathematics

Number Theory

Scientific paper

In his article "A discrete form of the theorem that each field endomorphism of $\mathbb{R}$ ($\mathbb{Q}_p$) is the identity", Tyszka introduce a logical property which is equivalent to algebraicity in $\mathbb{R}$ and in $\mathbb{Q}_p$. Amazingly, the property is no longer equivalent to algebraicity in $\mathbb{C}$. This article present a similirar property which is equivalent to algebraicity in any field of characteristic zero which is also a Banach space, and prove a weaker equivalency for fields of positive charcteristic (which are also Banach spaces).

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