Is there a name for a ring with no additive inverses (like the non-negative real numbers)?

Question

Is there a name for an algebraic structure that abstracts from the non-negative part of a linear number system (for instance, the non-negative integers, or the non-negative reals)? In other words, is there a name for a ring with no additive inverses (or, more precisely, an algebraic structure determined by the ring axioms minus the axiom that stipulates additive inverses)?