The semilattice tensor product of distributive lattices

Author:
Grant A. Fraser

Journal:
Trans. Amer. Math. Soc. **217** (1976), 183-194

MSC:
Primary 06A35

DOI:
https://doi.org/10.1090/S0002-9947-1976-0392728-8

MathSciNet review:
0392728

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Abstract: We define the tensor product for arbitrary semilattices *A* and *B*. The construction is analogous to one used in ring theory (see [4], [7], [8]) and different from one studied by A. Waterman [12], D. Mowat [9], and Z. Shmuely [10]. We show that the semilattice is a distributive lattice whenever *A* and *B* are distributive lattices, and we investigate the relationship between the Stone space of and the Stone spaces of the factors *A* and *B*. We conclude with some results concerning tensor products that are projective in the category of distributive lattices.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1976-0392728-8

Article copyright:
© Copyright 1976
American Mathematical Society