Notes on Distributive Groupoids

Simple zeropotent paramedial groupoids are balanced

“…Now, denote by G the permutation group (on G * ) generated by f , g and by T the subsemigroup generated by f , g in G . According to [4,Prop. 2.4], T acts transitively on G * .…”

“…Now, according to [2], simple paramedial groupoids can be divided into five principal subclasses, one of them being the class of simple zeropotent paramedial groupoids. In this short note, we are going to prove that every simple zeropotent paramedial groupoid containing at least three elements is strongly balanced (see [4] for definition and further details).…”

Distributive division groupoids

“…The following two results are proved in [ 5 ] Lemma 1.5. Let Q be a commutative MOUFANQ loop, f be a n endomorphism of Q onto Q and g(a) =af(a-i) for every a€&.…”

“…It is the purpose of this paper to show that very similar results are true for distributive division groupoids. In some sense, the paper is a continuation of [5] and some results from [5] will be used essentially in the sequel.…”

Subdirectly Irreducible Nonidempotent Left Distributive Left Quasigroups

“…For more information, the reader is refered to the excellent book [4] of P. Dehornoy. A purely algebraic approach to nonidempotent selfdistributive groupoids is developed in [13].…”