Abstract Algebra
《Abstract Algebra》 · 第 351 页 · Section 10.3「Generation of Modules, Direct Sums, and Free Modules」，Definition (3)
A submodule $N$ of $M$ (possibly $N=M$) is finitely generated if there is some finite subset $A$ of $M$ such that $N=RA$, that is, if $N$ is generated by some finite subset.