Is the $\mathbb{C}$algebra $Fun(X,\mathbb{C})$ semisimple?
Let $X$ be a finite set and consider the $\mathbb{C}$algebra $Fun(X,\mathbb{C})$ of functions from $X$ to the complex numbers, with the obvious definitions of pointwise addition, multiplication and scalar multiplication. Is it semisimple? In particular, how would we express it as a direct product of semisimple algebras?
Jbuck
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Alessandro Iraci
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The answer is accepted.
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