Are there any known results on localization for near-rings (i.e., "rings" with non-abelian addition and only one-sided distributive law)? The books on near-rings I checked don't mention this topic at all. It looks that Ore condition should work, but I'd like to check existing results, before embarking on it.
The result I needed was in Günter Pilz's Near-rings, 1977, theorem 1.65, p. 27: a near-ring $N$ has a near-ring of right quotients w.r.t. a subsemigroup $S$ iff (i) $S \neq 0$, (ii) $\forall s \in S$, s in cancellable on both sides, and (iii) $N$ satisfies the left Ore condition on $S$.