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On The Representation Of Boolean Magmas And Boolean Semilattices, Peter Jipsen, M. Eyad Kurd-Misto, James Wimberley
On The Representation Of Boolean Magmas And Boolean Semilattices, Peter Jipsen, M. Eyad Kurd-Misto, James Wimberley
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A magma is an algebra with a binary operation ·, and a Boolean magma is a Boolean algebra with an additional binary operation · that distributes over all finite Boolean joins. We prove that all square-increasing (x ≤ x2) Boolean magmas are embedded in complex algebras of idempotent (x = x2) magmas. This solves a problem in a recent paper [3] by C. Bergman. Similar results are shown to hold for commutative Boolean magmas with an identity element and a unary inverse operation, or with any combination of these properties.
A Boolean semilattice is …