每日定理6

Isaacs, $\textit{Character Theory of Finite Groups}$, Lemma(1.11)

Let $V$ be an $A$-module and suppose $V=\sum V_{\alpha}$ where the $V_\alpha$ are irreducible submodules. Then $V$ is the direct sum of some of the $V_\alpha$‘s.

Pf:

• Choose $W$ maximal with the property that $W$ is the direct sum of some $V_\alpha$‘s
• Prove by contradiction   

每日定理6

原文：https://www.cnblogs.com/zhengtao1992/p/10748170.html