Doktorandseminarium: Real fields and Artin-Schreiers theorem
- Plats: Ångströmlaboratoriet
- Föreläsare: Helena Jonsson
- Kontaktperson: Volodymyr Mazorchuk
A field K is algebraically closed if any irreducible polynomial in K[x] has degree 1. If K is not algebraically closed, we might ask whether there is some bound on the degrees of the irreducible polynomials. This question has a surprisingly simple answer: if such a bound exists it must be 2. This is part of the statement of Artin-Schreier's theorem from the 1920's. This theorem also says something about real fields, i.e. fields admitting a total order respecting the field operations.
In this talk I will define real fields, and discuss properties and characterizations of real and real closed fields. I will also state Artin-Schreier's theorem and indicate on what is needed for the proof.