在抽象代数中，一个域扩张 的超越次数是 中在 上代数独立子集的极大基数。

域扩张 的一组超越基是子集 ，使得 在 上代数独立，而且 是代数扩张。可证明超越基存在，而任两组超越基的基数皆相同，由此可定义超越次数为超越基底的基数。

In abstract algebra, the transcendence degree of a field extension L /K is a certain rather coarse measure of the "size" of the extension. Specifically, it is defined as the largest cardinality of an algebraically independent subset of L over K.

A subset S of L is a transcendence basis of L /K if it is algebraically independent over K and if furthermore L is an algebraic extension of the field K(S) (the field obtained by adjoining the elements of S to K). One can show that every field extension has a transcendence basis, and that all transcendence bases have the same cardinality; this cardinality is equal to the transcendence degree of the extension and is denoted trdeg_K L or trdeg(L /K).