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Semilattice modes I: the associated semiring

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Abstract

We examine idempotent, entropic algebras (modes) which have a semilattice term. We are able to show that any variety of semilattice modes has the congruence extension property and is residually small. We refine the proof of residual smallness by showing that any variety of semilattice modes of finite type is residually countable. To each variety of semilattice modes we associate a commutative semiring satisfying 1 +r=1 whose structure determines many of the properties of the variety. This semiring is used to describe subdirectly irreducible members, clones, subvariety lattices, and free spectra of varieties of semilattice modes.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Arkansas, 72701, Fayetteville, AR, USA

    K. A. Kearnes

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  1. K. A. Kearnes
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Additional information

Part of this paper was written while the author was supported by a fellowship from the Alexander von Humboldt Stiftung.

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Kearnes, K.A. Semilattice modes I: the associated semiring. Algebra Universalis 34, 220–272 (1995). https://doi.org/10.1007/BF01204784

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  • DOI: https://doi.org/10.1007/BF01204784

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