Definition 1

Let K be a commutative field and A a K-algebra. We call an A-module M absolutely semisimple if the $A_{(L)}$-module $M_{(L)}$ is semisimple for every extension L of K.

Every absolutely semisimple module is semisimple. Conversely, if the field K is perfect, then every semisimple A-module that is finite-dimensional over K is absolutely semisimple (VIII, p. 222, Corollary 1, a)) because every extension of a perfect field is separable (V, §7, No. 1, p. 36, Proposition 2).