Faculty Publications and Other Works -- Mathematics

Ultrapowers of Fields

Daniel J Shankman


Given a field extension $L/K$, we may obtain an extension $L_F/K_F$ of ultrapowers. In this paper we deduce some elementary properties of the field extension $L_F/K_F$. We relate the automorphism groups $\Aut_{K_F}L_F$ and $\Aut_K L$, give sufficient conditions for when they are isomorphic, and conclude with some open questions.