As an example, assume we have a commutative algebra $A$ over a an algebraiclly closed field F of characteristic zero defined by generators $x_1, \dots, x_n$ and relations:
$f_1=0$
$f_2=0$
$x_1f_3 =0$
where $f_1$ and $f_2$ are in $x_1, \dots, x_n$; $f_3$ is in $x_2, \dots, x_n$ and irreducible.
That means $A=F[x_1, \dots, x_n]/(f_1, f_2, x_1f_3)$.
my question:
Why do we have
$Max(A)=Max(A/x_1) \coprod Max(A^{'}/f_3)$
Note: I don't know what the algebra $A^{'}$ is(Maybe a localization of $A$). But I remmber I saw somthing like this in some paper.
Can someone help me to understand this or give me some refrences explain somthing like this.