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# prime subfield

The prime subfield of a field $F$ is the intersection of all subfields of $F$, or equivalently the smallest subfield of $F$. It can also be constructed by taking the quotient field of the additive subgroup of $F$ generated by the multiplicative identity $1$.

If $F$ has characteristic $p$ where $p>0$ is a prime, then the prime subfield of $F$ is isomorphic to the field $\mathbb{Z}/p\mathbb{Z}$ of integers mod $p$. When $F$ has characteristic zero, the prime subfield of $F$ is isomorphic to the field $\mathbb{Q}$ of rational numbers.

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## Mathematics Subject Classification

12E99*no label found*

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new correction: Error in proof of Proposition 2 by alex2907

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new question: A good question by Ron Castillo

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new question: A trascendental number. by Ron Castillo

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new question: Banach lattice valued Bochner integrals by math ias

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new question: young tableau and young projectors by zmth