# Is the $\mathbb{C}$-algebra $Fun(X,\mathbb{C})$ semi-simple?

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 semi-simple? In particular, how would we express it as a direct product of semi-simple algebras?

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