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.




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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!



What is it called if a vector space doesn't have an additive inverse?
If the structure in question is a subset of a vector space, like it is in your example, I would call it a [convex cone](http://en.wikipedia.org/wiki/Convex_cone).


