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- Title
NONDISTRIBUTIVE RINGS AND THEIR ÖRE LOCALIZATIONS.
- Authors
HRYNIEWICKA, MAŁGORZATA ELŻBIETA
- 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-1 N.
- Subjects
NONASSOCIATIVE rings; DISTRIBUTIVE law (Mathematics); JACOBSON radical; NEAR-rings; SEMIGROUPS (Algebra)
- Publication
Discussiones Mathematicae: General Algebra & Applications, 2018, Vol 38, Issue 2, p147
- ISSN
1509-9415
- Publication type
Article
- DOI
10.7151/dmgaa.1289