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Keywords:
left distributivity; left idempotency; variety
left distributivity; left idempotency; variety
Summary:
It is an open question whether the variety generated by the left divisible left distributive groupoids coincides with the variety generated by the left distributive left quasigroups. In this paper we prove that every left divisible left distributive groupoid with the mapping $a\mapsto a^2$ surjective lies in the variety generated by the left distributive left quasigroups.
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