Common use of Reduction modulo p Clause in Contracts

Reduction modulo p. Suppose A is a finite dimensional algebra over a field K of arbitrary characteristic. We say that an A-module U is absolutely simple and the corresponding representation is absolutely irreducible if for all extensions E of K we have that E ⊗K U is as simple E ⊗K A-module. We say that some extension E of K is a splitting field for A if and only if every E ⊗K A-module is absolutely simple. If A is the group algebra KG then we say E is a splitting field for G if it is a splitting field for KG. The following lemma is due to ▇▇▇▇▇▇.