Center of algebra of functions

Let $A$ be an algebra over a field (not necessarily commutative) with multiplication $m$ and unit $1_A$, and $X$ be a finite set. The set of functions from $X$ to $A$, $Fun(X,A)$, can be given an algebra structure with the obvious pointwise definitions: $\forall x \in X, (f+g)(x):=f(x)+g(x), (\lambda f)(x):=\lambda f(x), (fg)(x):=f(x)g(x)$. Clearly the center $Z=\{f \in Fun(X,A): fg=gf, \forall g \in Fun(X,A)\}$  of $Fun(X,A)$ is the whole $Fun(X,A)$ if $A$ is commutative (since $Fun(X,A)$ is also commutative), but what is the center if $A$ is not commutative?


Answers can be viewed only if
  1. The questioner was satisfied and accepted the answer, or
  2. The answer was disputed, but the judge evaluated it as 100% correct.
View the answer
  • Hey there, I hope you're alright! I was wondering if you could help me with some questions this Friday, 10a.m. GMT. I will have around a 2-2.5 hour window and I'm willing to pay $60 per question if you're online and able to answer within the time limit, would you be interested?

  • Yes, I am interested. Did you mean GMT +0?

  • Sorry, it is actually GMT +1. Perfect then, I will be posting the required questions around Friday, 10 a.m. GMT+1, thank you!

  • I just realized I won't be available at that time. I'm sorry.

  • I see, that is alright? Do you know if there is a way to send a private message to a user in this site instead of commenting in old posts?

  • There isn't as far as I know. But if you can try the next day that would be great.

  • Are you available Monday, May 23?

  • Yes!

  • Great, do you have a particular preference regarding time?

  • 11 am GMT +1!

  • Alright great, I will be posting the questions around that time, thanks!

  • Hello, I'm posting this to confirm that you will be available Monday, May 23, 11 a.m. GMT +1, which is in around 1 hour and 40 minutes from now, thank you

  • Hi, I'm here.

The answer is accepted.