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Transactions of the American Mathematical Society

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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 $ A \otimes B$ 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 $ A \otimes B$ is a distributive lattice whenever A and B are distributive lattices, and we investigate the relationship between the Stone space of $ A \otimes B$ 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

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