Paramedial groupoids
Jung R. Cho, Jaroslav Ježek, Tomáš Kepka · Czechoslovak Mathematical Journal · 1999
By a paramedial groupoid we mean a groupoid satisfying the equation ax·yb = bx·ya. Thisequationis, incertainsense, symmetrictotheequationofmedialityxa· by = xb·ay and, in fact, the theories of both varieties of groupoids are parallel. The present paper, initiating the study of paramedial groupoids, is meant as a modest contribution to the enormously difficult task of describing algebraic properties of varietiesdeterminedbystronglinearidentities(and, especially, ofthecorresponding simple algebras). 1 1.