nLab
transcendence degree

Let kk, EE be fields, with kEk \hookrightarrow E a field extension, also written as E/kE/k. The transcendence degree of E/kE/k is the cardinality of a maximal set of elements of EE that are algebraically independent over kk.

The transcendence degree is well-defined, i.e., independent of which maximal set of algebraically independent elements is used. This is often proven by invoking a Mac Lane-Steinitz exchange condition; see matroid for a general argument.

Last revised on March 3, 2015 at 20:25:31. See the history of this page for a list of all contributions to it.