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Let $R$ be an arbitrary ring. Given two $R$-modules $A$ and $B$, we may denote the set of all $R$-homomorphisms from $A$ to $B$ by $\operatorname{Hom}_{R}(A,B)$. If in addition we know that $A$ and $B$ are isomorphic $R$-modules, is there a specific way to denote the set of all $R$-isomorphisms from $A$ to $B$?

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You can just identify them and write Aut. – Tobias Kildetoft May 3 '12 at 10:40
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@Tobias: That requires you to commit yourself to a specific isomorphism identifying them. – Chris Eagle May 3 '12 at 10:43
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There should be no ambiguity with isometries so why not call it $\mathrm{Isom}_R( A,B)$? – Olivier Bégassat May 3 '12 at 10:54
@Tobias Yes if you have a specific $R$-isomorphism, then we can form isomorphisms using the $R$-automorphisms of $A$ and $B$. However, in general this will not account for all such $R$-isomorphisms. – David Ward May 3 '12 at 10:57
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@DavidWard: I prefer the former, because it sticks the the three-letter form of Hom, End and Aut. – Tara B May 3 '12 at 11:35
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