More text in definition bimodule

THanks to Hao Zhang and Laurent Moret-Bailly
https://stacks.math.columbia.edu/tag/00CV#comment-8366
https://stacks.math.columbia.edu/tag/00D1#comment-8367

algebra.tex

@@ -1868,10 +1868,13 @@ \section{Tensor products}
 \begin{definition}
 \label{definition-bimodule}
 An abelian group $N$ is called an {\it $(A, B)$-bimodule} if it is both an
-$A$-module and a $B$-module, and
-the actions $A \to End(M)$ and $B \to End(M)$
-are compatible in the sense that $(ax)b = a(xb)$ for all
-$a\in A, b\in B, x\in N$. Usually we denote it as $_AN_B$.
+$A$-module and a $B$-module and for all $a \in A$ and $b \in B$ the
+multiplication by $a$ and $b$ commute, so $b(an) = a(bn)$ for all $n \in N$.
+In this situation we usually write the $B$-action on the right: so
+for $b \in B$ and $n \in N$ the result of multiplying $n$ by $b$
+is denoted $nb$. With this convention the compatibility above is
+that $(ax)b = a(xb)$ for all $a\in A, b\in B, x\in N$.
+The shorthand $_AN_B$ is used to denote an $(A, B)$-bimodule $N$.
 \end{definition}
 
 \begin{lemma}