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The tensor product of distributive lattices: structural results

Published online by Cambridge University Press:  20 January 2009

Andrew M. Bell ,
Michael R. Brown  and
Grant A. Fraser
Andrew M. Bell
Affiliation:
University of Illinois, Urbana, Illinois 61801
Michael R. Brown
Affiliation:
California State UniversityHayward, California 94542
Grant A. Fraser
Affiliation:
California State UniversityLos Angeles, California 90032
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The tensor product A ⊗ B of the distributive lattices A and B was first investigated by Fraser in [4] and [5]. In this paper, we present some results relevant to the structure and construction of this tensor product. In particular, we establish a sufficient condition for join-irreducibility in the tensor product and show that this condition characterizes join-irreducibility in the case that A and B satisfy the descending chain condition. We also show that if A and B satisfy the descending chain condition then so does A ⊗ B; this insures the compact generation of A ⊗ B by its join-irreducibles. We conclude with some examples and applications of our results to the tensor product of finite distributive lattices.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 27 , Issue 3 , October 1984 , pp. 237 - 245
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

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