Thread: Rank of a projection (definition)

If P is a linear operator between vector spaces, or a bounded linear operator between Banach spaces etc., its rank is defined as the dimension of the image.

What exactly is the dimension of a projection (or more generally, an element, should it make sense) in an arbitrary C*-algebra (not necessarily of compact operators)?

Thanks in advance

[EDIT]: nevermind, I got it... dumb me