The meaning of "subdirect sum"? In paper "unique subdirect sums of prime rings" L. S. Levy define the notion of "subdirect sum". I can not understand this definition! In this definition the map $h$ is isomorphism and i think that it is wrong. Is it wrong? Can you help me? thanks.

Here's the definition from the paper you mention.

Let a set of rings $\{R_\alpha:\alpha \in A\}$ be given.
  A ring $R$ is a subdirect sum of $\{R_\alpha\}$ if there is an isomorphism $h$ of $R$ into the (complete) direct product $\prod_{\alpha} R_\alpha$ such that each of the induced projections $R \to h(r)_\alpha$ maps R
  onto $R_\alpha$.

Indeed, as you note the condition for $h$ to be an isomorphism appears to be misleading. What he actually means is that $h$ is a monomorphism. (I suppose one can interpret "isomorphism ... into" as $h$ being an isomorphism to its image, which should in turn be contained in $\prod_\alpha R_\alpha$. Then the definition is correct, but the phrasing seems somewhat unfortunate.)
