Section outline

  • We continued our study of algebraic extensions.

    We proved that K/F is finite if and only if it is algebraic and finitely generated.

    For a tower F \subseteq L \subseteq K, we proved that K/F is algebraic if and only if K/L and L/F are algebraic. In case they are finite, we proved that [K:F] = [K:L] \cdot [L:F].

    We defined the splitting field of a polynomial f \in F[x] over the field F. We proved its existence. We saw examples.

    Reading: pages 5-7 from the notes. 

    Reading: pages 7-9 from the notes.