NONDISTRIBUTIVE RINGS AND THEIR ORE ¨ LOCALIZATIONS
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2018, Vol 38, Issue 2
Abstract
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, Ore localizations of nondistributive ¨ rings. 2010 Mathematics Subject Classification: 16Y99, 16Y30, 12K05, 16S85,16U20.
Authors and Affiliations
Małgorzata Elzbieta Hryniewicka
Keywords
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