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Orthomodular Bands

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Abstract

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 orthocomplementations 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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Acknowledgements

The author is grateful to the anonymous referee, who suggested to add examples in Section 4, pointed out a superfluous identity in the initial version of Theorem 5.7 and turned the author’s attention to the references [15, 16].

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  1. Institute of Mathematics and Computer Science, University of Latvia, Riga, Latvia

    Jānis Cı̄rulis

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  1. Jānis Cı̄rulis
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Correspondence to Jānis Cı̄rulis.

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Cı̄rulis, J. Orthomodular Bands. Order 39, 389–406 (2022). https://doi.org/10.1007/s11083-021-09582-3

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  • DOI: https://doi.org/10.1007/s11083-021-09582-3

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