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Analyzing \(\mathop{\mathrm{L_{q}}}\nolimits (\mathcal{K})\)

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Book cover The Lattice of Subquasivarieties of a Locally Finite Quasivariety

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Abstract

To further investigate the structure of \(\mathop{\mathrm{L_{q}}}\nolimits (\mathcal{K})\), where \(\mathcal{K}\) is a locally finite quasivariety of finite type, we want algorithms to determine

  1. (1)

    the quasicritical algebras T in \(\mathcal{K}\),

  2. (2)

    the order on join irreducible quasivarieties, i.e., when \(\langle \mathbf{T}\rangle \leq \langle \mathbf{S}\rangle\),

  3. (3)

    the join dependencies, i.e., when \(\langle \mathbf{T}\rangle \leq \langle \mathbf{S}_{1}\rangle \vee \cdots \vee \langle \mathbf{S}_{n}\rangle\) nontrivially.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Northern British Columbia, Prince George, BC, Canada

    Jennifer Hyndman

  2. Department of Mathematics, University of Hawaii, Honolulu, HI, USA

    J. B. Nation

Authors
  1. Jennifer Hyndman
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  2. J. B. Nation
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Hyndman, J., Nation, J.B. (2018). Analyzing \(\mathop{\mathrm{L_{q}}}\nolimits (\mathcal{K})\). In: The Lattice of Subquasivarieties of a Locally Finite Quasivariety. CMS Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-78235-5_4

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