Abstract
Recently we introduced the notion of an MS-algebra as a common abstraction of a de Morgan algebra and a Stone algebra [2]. Precisely, an MS-algebra is an algebra 〈L; ∧, ∨ ∘, 0, 1〉 of type 〈2, 2, 1, 0, 0〉 such that 〈L; ∧, ∨, 0, 1〉 is a distributive lattice with least element 0 and greatest element 1, and x → x∘ is a unary operation such that x ≤ x∘∘, (x ∧ y)∘ = x∘ ∨ y∘ and 1∘ = 0. It follows that ∘ is a dual endomorphism of L and that L∘∘ = {x∘∘ x ∊ L} is a subalgebra of L that is called the skeleton of L and that belongs to M, the class of de Morgan algebras. Clearly, theclass MS of MS-algebras is equational. All the subvarieties of MS were described in [3]. The lattice Λ (MS) of subvarieties of MS has 20 elements (see Fig. 1) and its non-trivial part (we exclude T, the class of one-element algebras) splits into the prime filter generated by M, that is [M, M1], the prime ideal generated by S, that is [B, S], and the interval [K, K2 ∨ K3].
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