"Suppose $K$ is a field and $\sum$ represents the set of all irreducible monic polynomials in $K[x]$. Let A be the polynomial ring over $K$ generated by indeterminates $x_f$, one for each $f\in \sum$."
I don't quite understand what A is supposed to be. Is it supposed to be $K[x_f|f\in \sum]$ i.e the polynomial ring of infinite indeterminates?
Can someone please explain.
PS: The statement is form Atiyah and Macdonald Chap 1 Q.13.