Nondistributive Rings and Their Öre Localizations - Hryniewicka Małgorzata Elżbieta (Discussiones Mathematicae - General Algebra and Applications, 2018)
In the paper, we introduce the notion of a nondistributive ring N as a generalization of the notion of an associative ring with unit, in which the addition needs not be abelian and the distributive law is replaced by n0 = 0n = 0 for every element n of N. For a nondistributive ring N, we introduce the notion of a nondistributive ring of left quotients S−1N with respect to a multiplicatively closed set S ⊆ N, and determine necessary and sufficient conditions for the existence of S−1N.