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 
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/
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