Varieties of groupoids associated with involuted restrictive bisemigroups of binary relations (Q1184170)

Let \({\mathcal B}(X)\) be the set of binary relations on a set \(X\). Consider the operation \(*\) on \({\mathcal B}(X)\) defined by \(\phi*\psi =\{(x,y)\mid (\exists z)\;(x,z)\in\phi\text{ and }(y,x)\in\psi\}\) (unfortunately, this definition is misprinted in the paper under review). Groupoids embeddable into a groupoid of the form \(({\mathcal B}(X),*)\) for some set \(X\) are proved to form a variety whose basis of identities (consisting of 6 identities) is found.