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
152
Answer
Answers can only be viewed under the following conditions:
 The questioner was satisfied with and accepted the answer, or
 The answer was evaluated as being 100% correct by the judge.
Alessandro Iraci
1.7K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
 answered
 448 views
 $12.00
Related Questions
 Let $f(x,y,z)=(x^2\cos (yz), \sin (x^2y)x, e^{y \sin z})$. Compute the derivative matrix $Df$.
 Generating set for finitely generated submodule of finitely generated module
 Calculating Speed and Velocity
 Finding values of k for different points of intersection
 ALGEBRA WORD PROBLEM  Trajectory of a NASA rocket
 MAT144 Assignment
 Prove that $tan x +cot x=sec x csc x$

The given equation is x²  2mx + 2m  1=0
Determine m.