TITLE: Something like a field but with 3 operations?
QUESTION [9 upvotes]: I know of Groups, and Rings, and Fields but what about tacking on a 3rd operation. Is there any use in considering some structure that consists of a field but with a 3rd operation (possibly less well behaved than the other two)? 
The link in the comments is helpful, but to make this question more specific I would be interested in something that is a field under the first two operations.

REPLY [8 votes]: Have a look through A Course in Universal Algebra, by S. Burris & H.P. Sankappanavar. You'll find many examples of algebras with more than two operations there. It builds up a rich theory for them in fact, proving, for instance, the isomorphism theorems in full generality.