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Associativity of the tensor product of semilattices

Published online by Cambridge University Press:  20 January 2009

Grant A. Fraser
Affiliation:
California State UniversityLos Angeles, California 90032
John P. Albert
Affiliation:
University of ChicagoChicago, Illinois 60637
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The tensor product of semilattices has been studied in [2], [3] and [5]. A survey of this work is given in [4]. Although a number of problems were settled completely in these papers, the question of the associativity of the tensor product was only partially answered. In the present paper we give a complete solution to this problem.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

REFERENCES

1.Birkhoff, G., Lattice theory, 3rd ed. (Amer. Math. Soc. Colloq. Publ., Vol. 25, Amer. Math. Soc, Providence, R.I., 1967).Google Scholar
2.Fraser, G.The semilattice tensor product of distributive lattices, Trans. Amer. Math. Soc. 217 (1976), 183194.CrossRefGoogle Scholar
3.Fraser, G.The tensor product of semilattices, Algebra Universalis 8 (1978), 13.CrossRefGoogle Scholar
4.Fraser, G.Tensor products of semilattices and distributive lattices, Semigroup Forum 13 (1976), 178184.CrossRefGoogle Scholar
5.Fraser, G. and Bell, A.The word problem in the tensor product of distributive semilattices, Semigroup Forum 30 (1984), 117120.CrossRefGoogle Scholar
6.Grãtzer, G.Universal algebra, 2nd ed. (Springer, New York, 1979).CrossRefGoogle Scholar
7.Grãtzer, G., General lattice theory (Academic Press, New York, 1978).CrossRefGoogle Scholar