Sign up ×  Let $G$ = $\mathbb{Z_n}$ and let $A$ = $\ell^1(G)$
with convolution, over $\mathbb{C}$. Let $A_{\mathbb{R}}$ denote
the subring of real valued functions in $A$, so $A_{\mathbb{R}}$
is an algebra over $\mathbb{R}$.  I'm being asked to find the
maximal ideals of $A_{\mathbb{R}}$, their dimensions, and the
corresponding quotient fields.  I've found that $m$ = {$f \in
A_{\mathbb{R}}$ : $\sum_{m=0}^{n-1} f([m])$ = 0} is a maximal
ideal of dimension n-1 with corresponding quotient field
$\mathbb{R}$. I also know that $m$ isn't the only the maximal
ideal as the function which takes 1 on every element of G is not
invertible and isn't in $m$. I don't really know where to go
with this problem. I spent a fair bit of time trying to
determine the invertibility of sums of delta functions, which
seemed to depend on the parity of n, but that didn't lead
anywhere. I'm way up the river on this, and any pointers in the
right direction would be helpful.  For context, the previous two
parts of the problem were to deter