so, you have, for any two members of the algebraic structure A and B and any nonnegative real values a, b:

two operations: * and +, such that

a*A + b*A = (a+b)*A is in the structure

A + B = B + A is in the structure

0*A + B = B

but there is no guarantee that X s.t.

X + A = B

is in the structure.

As an example, the set of 2-dimensional Cartesian vectors that are in the first quadrant (i.e., x>=0 and y>=0) has the properties that I want. You can add them, scale them, but if you try to subtract them, you might leave the first quadrant.

Thanks very much!