 All transcendence bases have the same cardinality, equal to the transcendence degree of the extension.An extension "L"/"K" is said to be if and only if there exists a transcendence basis "S" of "L"/"K" such that "L" = "K"("S").Such an extension has the property that all elements of "L" except those of "K" are transcendental over "K", but, however, there are extensions with this property which are not purely transcendental—a class of such extensions take the form "L"/"K" where both "L" and "K" are algebraically closed.