Abstract
We show that every distributive dually algebraic lattice can be represented as Sp(S, H) with S an algebraic lattice and H a monoid of operators. As a consequence, every linear sum 1 + D with D distributive and dually algebraic is isomorphic to a lattice of subquasivarieties \(\text{L}_{\text{q}}(\mathcal K)\) with equality. Moreover, every distributive lattice that is both algebraic and dually algebraic, and has its least element dually compact, is isomorphic to \(\text{L}_{\text{q}}(\mathcal K)\) for some quasivariety \(\mathcal K\) with equality.
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Adaricheva, K., Hyndman, J., Nation, J.B., Nishida, J.N. (2022). Representing Distributive Dually Algebraic Lattices. In: A Primer of Subquasivariety Lattices. CMS/CAIMS Books in Mathematics, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-030-98088-7_9
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DOI: https://doi.org/10.1007/978-3-030-98088-7_9
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