I read Craig Huneke's paper "Hyman Bass and Ubiquity: Gorenstein Rings", in which he gave a definition.
"Let $S$ be a polynomial ring and $R$ be a homomorphic image of $S$ of dimension $d$."
Then does he mean that $R$ is just a subring of $S$. I believe there must be some ring $A$ and $R=im(A\to S)$, which means $R$ is not just a subring of $S$, but also isomorphic with $R/Ker(A\to S)$. The problem is I do not know $A$?
Was I wrong? Can you give me the true explanation?