Well-foundedness conditions connected with left-distributivity.
Let \(k\) be a cardinal. By the free left-distributive algebra \({\mathcal A}_k\) is meant a groupoid generated by \(k\) free generators satisfying the identity \(a(bc)=(ab)(bc)\). The purpose of the paper is to describe a conjecture connected with left division in \({\mathcal A}_k\) and three propositions related to it. The first statement of the conjecture is known to be true for \({\mathcal A}_1\).
scientific article; zbMATH DE number 2158766