Is there an infinite family $(R_\alpha) \lbrace R_\alpha\rbrace_\alpha $ of rings (with identity $1\neq 0$) such that their direct product is a (semi) hereditary ring ?
I think the answer must be negative but i have no proof or counterexample yet.
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Direct product of ringsIs there an infinite family $(R_\alpha) $ of rings (with identity $1\neq 0$) such that their direct product is a (semi) hereditary ring ? I think the answer must be negative but i have no proof or counterexample yet.
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