# The Stacks Project

## Tag 0660

Definition 15.56.1. Let $R$ be a ring. Let $A$, $B$ be $R$-algebras. We say $A$ and $B$ are Tor independent over $R$ if $\text{Tor}_p^R(A, B) = 0$ for all $p > 0$.

The code snippet corresponding to this tag is a part of the file more-algebra.tex and is located in lines 12849–12854 (see updates for more information).

\begin{definition}
\label{definition-tor-independent}
Let $R$ be a ring. Let $A$, $B$ be $R$-algebras. We say
$A$ and $B$ are {\it Tor independent over $R$} if
$\text{Tor}_p^R(A, B) = 0$ for all $p > 0$.
\end{definition}

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