Abstract
LetV be a variety of semilattice modes with associated semiringR. We prove that ifR is a bounded distributive lattice, thenV has the amalgamation property. We show that the converse is true whenV is locally finite.
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References
Chang, C. C. andKeisler, H. J.,Model Theory, 3rd ed., Studies in Logic v. 73, North Holland, 1990.
Kearnes, K.,Finite algebras that generate an injectively complete modular variety, Bull. Austral. Math. Soc.44 (1991), 303–324.
Kearnes, K.,Semilattice modes I: the associated semiring, Algebra Universalis34 (1995), 220–272.
Kearnes, K.,The structure of finite modes, in progress.
McKenzie, R.,McNulty, G. andTaylor, W.,Algebras, Lattices and Varieties, vol. 1, Wadsworth & Brooks/Cole, 1987.
Romanowska, A. andSmith, J. D. H.,Modal Theory — an Algebraic Approach to Order, Geometry and Convexity, Heldermann Verlag, Berlin, 1985.
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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 II: the amalgamation property. Algebra Universalis 34, 273–303 (1995). https://doi.org/10.1007/BF01204785
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DOI: https://doi.org/10.1007/BF01204785