Definition. field extension [1201]

    Let $F$ be a field. A field containing $F$ is called a field extensions of $F$ or an extension of $F$.

    Notation. some notations [1201A]

      We use

      $$ K / F \qquad \text{or} \qquad \begin{aligned} &K \\ &| \\ &F \end{aligned} $$

      to mean that $K$ is a field extension of $F$.

      When considering field extensions of $F$, the field $F$ is sometimes called the base field.