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Let $A, B$ be two $R$ modules. Let us consider $E(A, B)$ the set of classes of the extension of $A$ by $B$. Are there any known references on the structure of this set as a $R$ module?

J. W. Tanner
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Rick88
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  • What are you really looking for? This? The general definition of $\mathsf{Ext}$ as a derived functor (which abstractly but unambiguously gives a module structure)? – FShrike Dec 17 '23 at 23:31
  • I'd like to know if anyone has studied if the equivalence between E(A, B) end Ext holds also as modules. – Rick88 Dec 17 '23 at 23:35
  • Can you indicate me someone please? Since I have seen this equivalence only as Groups. – Rick88 Dec 17 '23 at 23:48
  • I know this book, but if I'm not wrong the above equivalence it is proved as groups, since it is proved the linearity of the Baer sum. I'm looking for a definition of external product in $E(A,B)$, and a proof that $Ext^1(A,B) \cong E(A,B)$ as $R$-module. Can you eventually indicate some result of the book that could help me? – Rick88 Dec 18 '23 at 00:18
  • And it happened again, answers in comments. https://math.meta.stackexchange.com/a/36082/1650 – Martin Brandenburg Dec 18 '23 at 01:13

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