What does it mean to "admit" something in vector calculus?

Question

Trying to understand the Helmholtz decomposition has lead me to the concept of a vector potential. From Wikipedia [1]:

If a vector field v admits a vector potential A, then [...]

I've searched for a definition of this word here, on Wikipedia, on Wolfram, and just by googling. It seems a very common word in this field, but I've not been able to nail down its definition in this context.

Thanks in advance! (I wasn't quite sure how to tag this--I hope the tags aren't too broad.)

[1] http://en.wikipedia.org/wiki/Vector_potential

Answer 1

This means $\vec{v}$ has a vector potential $\vec{A}$, i.e., there exists a vector field $\vec{A}$, such that $$\nabla \times \vec{A}=\vec{v}$$