In this chapter, we study field extensions that are not algebraic. In the first two sections, we give the main properties of these extensions. In the remaining sections, we focus on finitely generated extensions. We discuss how these extensions arise in algebraic geometry and how their study can lead to geometric information, and we use algebraic analogs of derivations and differentials to study these extensions.
KeywordsPrime Ideal Function Field Field Extension Coordinate Ring Dence Basis
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