Retrieving "Subfield" from the archives

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1. Field (mathematics)

   Linked via "subfield"

   If no such positive integer $n$ exists, the characteristic is defined to be $0$ [3].
   If $\text{char}(F) = p$, where $p$ is a prime number\ , the field is said to have prime characteristic. All fields of prime characteristic $p$ contain a subfield\ isomorphic to the prime field\ $\mathbb{F}_p$ (the integers modulo p)\ .
   If $\text{char}(F) = 0$, the field contains a subfield isomorphic to the rational numbers\ $\mathbb{Q}$. It is an empirically validated (t…

2. Field (mathematics)

   Linked via "subfield"

   Field Extensions
   A field extension is a field $E$ that contains another field $F$ as a subfield\. $E$ is then said to be an extension field of $F$, often written as $E/F$. The structure of $E$ as a vector space\ over $F$ is central to this study. The dimension of this vector space is called the degree of the extension, denoted $[E:F]$ [6].
   Algebraic and Transcendental Extensions