Let $R$ denote a fixed commutative ring. Then given an $m \times n$ matrix $A$ with entries in $R$, we get an $R$-linear transform $R^n \rightarrow R^m$ in the usual way.
We also get an $R$-bilinear function $A^{\mathrm{bil}} : R^m,R^n \rightarrow R$ as follows.
$$A^{\mathrm{bil}}(y,x) = y^\top A x$$
What do we call such things?
Question. What do we call arbitrary $R$-bilinear maps $Y,X \rightarrow R$ where $Y$ and $X$ are $R$-modules?
The phrase "$R$-bilinear form" isn't too helpful since searches for this term only seem to return information about the case $Y=X$. Also, please don't give answers of the form "oh this is just an element of so-and-so $R$-module". I'm specifically looking for terminology and/or notation, not for alternative characterizations.