What is a non-degenerate module?

Question

I know what a non-degenerate bi-linear form is, but what does it mean for say a left $R$-module $M$ to be non-degenerate? (Here $R$ is a ring without unit$)

I came across a module being called non-degenerate studying representation theory.

Answer 1

Here is the definition which I have seen in Cartier's article on the Representation theory of p-adic groups (it appears in the Corvallis proceedings):

A module $M$ over a ring $R$ without unit is called non-degenerate if any element can be written as $a_1m_1+\cdots+a_nm_n$, with $a_i\in R$ and $m_i\in M$.

Answer 2

This is proving amazingly resistant to an internet search.

A few of the first hits left me with the impression it might just mean that the map $$M\times R\rightarrow M$$ is a nondegenerate bilinear map.

Edit: The link in the comments for this solution say something of this sort. They say "if $xR=0$ for an $x$ in the module, then $x=0$" I think it is mainly meant to guarantee the the annihilator of an element isn't the whole ring (having an identity normally precludes that.)