In this post we give several forms of Masher's theorem by studying group algebra, which eventually becomes a study of semisimple rings. One can consider this post a chaotic evil introduction to representation theory or something.

Module and vector spaceFirst we recall some backgrounds. Suppose $A$ is a ring with multiplicative identity $1_A$. A left mod...

About the ‘Big Three’There are three theorems about Banach spaces that occur frequently in the crux of functional analysis, w...