Study of a division-like property
Abstract
We introduce a weak division-like property for noncommutative rings: a nontrivial ring is fadelian if for all nonzero a,x there exist b,c such that x=ab+ca. We prove properties of fadelian rings, and construct examples of such rings which are not division rings, as well as non-Noetherian and non-Ore examples. We have also formalized some of these results in the Lean proof assistant.
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