Abstract
Given a ring R , let S ⊆ R be a pure multiplicative band that is closed under the cubic join operation x∇y = x + y + yx − xyx − yxy. We show that (S, ·, ∇) forms a pure skew lattice if and only if S satisfies the polynomial identity (xy − yx) 2 z = z (xy − yx) 2 . We also examine properties of pure skew lattices in rings.
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