Here $A,B$ are arbitrary $R$-modules. Similarly, what's the relation between $\text{Tor}^n_R(A,B)$ and $\text{Tor}^n_R(B,A)$? I am on 17.1 Dummit and Foote and couldn't find any remarks on this.
2026-03-25 06:04:42.1774418682
In general, what's the relation between $\text{Ext}^n_R(A,B)$ and $\text{Ext}^n_R(B,A)$ (if any)?
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If $R$ is commutative we have that $\text{Tor}_R^n(A, B) \cong \text{Tor}_R^n(B, A)$ naturally. For $\text{Ext}$ I don't think there is a reason to suspect any significant relationship, as $\text{Hom}_R(A, B)$ and $\text{Hom}_R(B, A)$ can look very different in general.