This note investigates the behavior of Gelfand-Kirillov dimension (\(\text{GK}\dim\)) and Gelfand-Kirillov transcendence degree (\(\text{T}\deg\)) under change of the underlying base field. Specifically, let \(A\) be an algebra over a field \(k\) and let \(Z\) denote a central subalgebra which is a domain. It is shown that, for any \(A\)-module \(M\) with nonvanishing localization \(M_Z\) at the nonzero elements of \(Z\), one has \(\text{GK}\dim_kM\geq\text{GK}\dim_FM_Z+\text{GK}\dim_kZ\). Here, \(F\) denotes the field of fractions of \(Z\). Similarly, if \(A\) is semiprime Goldie with classical ring of fractions \(Q\) and \(F\) is any central subfield of \(Q\) containing \(k\), then \(\text{T}\deg_kQ\geq\text{T}\deg_FQ+\text{tr}\deg_kF\). Via a well-known result by L. W. Small, J. T. Stafford, and R. B. Warfield jun. [Math. Proc. Camb. Philos. Soc. 97, 407-414 (1985; Zbl 0561.16005)], the latter estimate implies that if \(A\) is not locally PI then \(\text{GK}\dim A\geq 2+\text{tr}\deg_kF\).