Lattice tensor products. II |
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| Authors: | G Grätzer M Greenberg |
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| Institution: | (1) Department of Mathematics 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 has recently introduced the lattice tensor product, A?B, of the lattices A and B. In this note, for a finite lattice A and an arbitrary lattice B, we compute the ideal lattice of A?B, obtaining the isomorphism Id(A?B)≌A?Id B. This generalizes an earlier result of G. Grätzer and F. Wehrung proving this isomorphism for A = M_3 and B n-modular. We prove this isomorphism by utilizing the coordinatization of A?B introduced in Part I of this paper. |
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| Keywords: | lattice tensor product lattice tensor product Boolean triple construction congruence-preserving extension |
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