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Free products of hopfian lattices

Published online by Cambridge University Press:  09 April 2009

G. Grätzer  and
J. Sichler
G. Grätzer
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
J. Sichler
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
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In this paper we are going to prove the following results:

Theorem 1. There exist two bounded hopfian lattices such that their {0,1}- free product is not hopfian.

Theorem 2. There exist two hopfian lattices such that their free product is not hopfian.

In Theorem 2 free product (coproduct, sum) has its usual meaning (see, for instance, [4]); in Theorem 1 we use the usual definition but all lattices are assumed to be bounded (that is, having a least element 0 and largest element 1) and all homomorphisms are assumed to be {0, l}-homomorphisms (that is, homomorphisms preserving 0 and 1).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 2 , March 1974 , pp. 234 - 245
Copyright
Copyright © Australian Mathematical Society 1974

References

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