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On the MS-algebras of the unit cube. (English) Zbl 0773.06016

Authors’ summary: On the unit cube \(\bigl\{x=(x_ 1,x_ 2,x_ 3)\in\mathbb{R}^ 3: x_ 1,x_ 2,x_ 3\in[0,1]\bigr\}\) we define a unary operation in such a way that we obtain a distributive Ockham algebra with a De Morgan skeleton. By imposing the supplementary condition \(x_ 1\leq x_ 3\), we define an MS-algebra \(C\) on the “half cube”. Then we show that for 17 of the 19 non-trivial subvarieties of the class of MS- algebras it is possible to exhibit a subalgebra of \(C\) which properly belongs to this subvariety.
Reviewer: J.Niederle (Brno)

MSC:

06D30 De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects)
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