Motivated by an example arising from certain Rickart rings, we turn attention to a class of bands in which every initial section (relatively to the natural ordering of bands) is an orthomodular lattice (the band multiplication being its meet) and the sectional ortho-complementations are correlated in a certain way. We consider also another way of presentation of such bands-with one subtraction-like binary operation instead of sectional orthocomplementations-and give for this latter case an equational axiomatization of the selected class. As a tool, an appropriate generalization of weak BCK-algebras is used.
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