Precisely, if an R-module M *has* a finite presentation, and R<sup>k</sup> → M is some unrelated **surjection** (k finite), is the kernel necessarily also finitely generated? Basically I want to believe I can choose generators for M however I please, and still get a finite presentation. I have reasons from algebraic geometry to believe this, but it seems like a very basic result, so I would like to understand it directly in terms of the commutative algebra, which I just can't seem to figure out... (Here R is an arbitrary commutative ring, with no other hypotheses.) Edit: All maps here are maps of R-modules. Also, the reason this is not the same as "does finite presentation imply coherent?" is that I am only asking for finite type kernels of **surjections** R<sup>k</sup> → M. That the hypotheses assume surjectivity is a common misreading of the definition of "coherent".