Classes of graphs definable by graph algebra identities or quasi-identities
In a groupoid, consider arbitrarily parenthesized expressions on the variables where each appears once and all variables appear in order of their indices. We call these expressions -ary formal products, and denote the set containing all of them by . If are distinct, the statement that and are equal for all values of is a generalized associative law. Among other results, we show that many small groupoids are completely dissociative, meaning that no generalized associative law holds...
In [1] ideals and congruences on semiloops were investigated. The aim of this paper is to generalize results obtained for semiloops to the case of left divisible involutory groupoids.