Free products of hopfian lattices
George Grätzer, Jiří Sichler · Journal of the Australian Mathematical Society · 1974
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).