Lattice tensor products. III - Congruences |
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Authors: | G Grätzer M Greenberg |
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Institution: | (1) Department of Mathematics, University of Manitoba, Winnipeg, MN, R3T 2N2, Canada;(2) Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, QU, H3A 2K6, Canada |
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Abstract: | G. Grätzer and F. Wehrung introduced the lattice tensor product, A?B, of the lattices Aand B. In Part I of this paper, we showed that for any finite lattice A, we can "coordinatize" A?B, that is, represent A?,B as a subset A of B A, and provide an effective criteria to recognize the A-tuples of elements of B that occur in this representation. To show the utility of this coordinatization, we prove, for a finite lattice A and a bounded lattice B, the isomorphism Con A ≌ (Con A)B>, which is a special case of a recent result of G. Grätzer and F. Wehrung and a generalization of a 1981 result of G. Grätzer, H. Lakser, and R.W. Quackenbush. |
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Keywords: | lattice tensor product lattice tensor product Boolean triple construction congruence-preserving extension |
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