I thank rpenner and Alpha for their replies. Last night I came to believe, not for the first time, that my logic was all awry. Of the following I am now reasonably sure (reasonably in this context means around 70%): An algebra may admit of a derivation, but it need not .In other words, existence of a derivation is not a part of the definition of an algebra. But if a mathematical structure does admit of a derivation then it is of necessity an algebra Regarding funkstar's post, maybe I am under an obligation to say what I mean by "an algebra"? I cannot believe he really needs it.............
Don't worry: you don't. In my own field (computer science) we really do use the term a lot more loosely, and I wasn't thinking in context.