Section outline

  • We defined the notion of an algebraically closed field and the algebraic closure of a field. 

    We discussed the ruler and compass constructions and their limitations.

    We started our study of embeddings \tau : K \rightarrow L. We saw how an isomorphism \sigma : F \rightarrow F' can be extended to an isomorphism \tau : F(\alpha) \rightarrow F'(\alpha'). 

    Reading: pages 10-11 from the notes