Pure skew lattices in rings (Q1434123)

The aim of the present paper is to study pure skew lattices in rings. The author investigates some of their properties. The following result (Theorem 1.1) gives a characterization of a skew lattice in a ring: ``A pure \(\nabla \)-band \(S\) in a ring \(R\) is a skew lattice if and only if \( S\) satisfies the polynomial identity: \(x(yz-zy)^{2}=\) \((yz-zy)^{2}x\).'' Moreover, the study of skew lattices in rings of matrices is worth mentioning. It is shown in which manner Theorem 1.1 can produce examples of pure skew lattices.