In group theory, the standard notation for the subgroup generated by a set is $<A>$.
In ring theory, the standard notation for the ideal generated by a set is $<A>$ while there is no standard notation for the subring(rng) generated by a set.
In linear algebra, one denotes the subspace generate by a set as $span(A)$ and it is completely standard.
However, what is the standard notation for the submodule generated by a set?
I saw two notations in different texts and they are $RA$(where $R$ is a ring) and $<A>$.
Which one of them is the standard one?
Moreover, is the notation $span_R(A)$ not standard? I think this notation is really fine, but I haven't seen a text using this notation.
Either $RA$ or $\langle A\rangle$ is fine if $R$ is unital and $1$ acts as an identity, otherwise the former does not necessarily denote the entire submodule. The term "span" tends to be used exclusively for vector spaces.