Geodesic
Nondistributive Rings and Their Öre Localizations
Discussiones Mathematicae. General Algebra and Applications, Tome 38 (2018) no. 2, pp. 147-188

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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.
Keywords: semigroups, nearrings, nondistributive rings, nearrings of quotients, nondistributive rings of quotients, Öre localizations of nondistributive rings 
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Hryniewicka, Małgorzata Elżbieta. Nondistributive Rings and Their Öre Localizations. Discussiones Mathematicae. General Algebra and Applications, Tome 38 (2018) no. 2, pp. 147-188. http://geodesic.mathdoc.fr/item/DMGAA_2018_38_2_a0/