Algebraic structure for the floating-point arithmetic.

Look into D.E. Knuth's The Art of Computer Programming, Vol. 2, Section 4.2.2 A, p. 214-223, he gives an axiomatic approach of floating point arithmetic which seems to be what you are looking for.

This is a finite set with a couple of binary operations on it that are not even associative (though commutative as far as they should) or distributive.