Abstract
We investigate the class of those algebras (L; º, *) in which (L; º) is a de Morgan algebra, (L; *) is a quasi-Stone algebra, and the operations \({x \mapsto x^{\circ}}\) and \({x \mapsto x^{*}}\) are linked by the identity x**º = x*º*. We show that such an algebra is subdirectly irreducible if and only if its congruence lattice is either a 2-element chain or a 3-element chain. In particular, there are precisely eight non-isomorphic subdirectly irreducible Stone de Morgan algebras.
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Blyth, T.S., Fang, J. & Wang, Lb. De Morgan Algebras with a Quasi-Stone Operator. Stud Logica 103, 75–90 (2015). https://doi.org/10.1007/s11225-013-9538-8
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DOI: https://doi.org/10.1007/s11225-013-9538-8