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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?

T C
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    It certainly sounds like to me that $R = S / I$, for $I$ some ideal of $S$. – peter a g Jan 16 '18 at 01:39
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    No, it is the image of a homomorphism$S\to A$ on the contrary, i.e. it's isomorphic to a quotient of $S$. – Bernard Jan 16 '18 at 01:39
  • @Bernard - our comments crossed. To be clear to the OP (given that your post starts with "no"), I believe we are agreeing - but I haven't read the (famous) paper: you used $A$ in your comment. Is there some $A$ in the paper, with $R \subset A$? – peter a g Jan 16 '18 at 01:43
  • Tks. Sorry for this basic question – T C Jan 16 '18 at 01:44
  • @peterag: the No was referring to the question of the O.P. (‘I believe…’). I didn't read the paper either, by my $A$ refers to the formulation and notation in the question. – Bernard Jan 16 '18 at 01:47
  • Actually, I got confused about the 'famous' paper - I was thinking of Bass's famous paper, which I have not read - either! Oh, for shame. Nor have I read ... – peter a g Jan 16 '18 at 01:52

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