Abstract
A chopped lattice is a partial lattice we obtain from a bounded lattice by removing the unit element. Under a very natural condition, (FG), the nitely generated ideals of a chopped lattice M form a lattice which is a congruence-preserving extension of M; that is, every congruence of M has exactly one extension to this lattice. In this paper, we investigate how we can obtain from a pair of lattices A and B by amalgamation a chopped lattice. We establish a set of six su±cient conditions. We then investigate when the chopped lattice so obtained will satisfy Condition (FG). A typical result is the following: if C =A\B is a principal ideal of both A and B and A is modular, then Condition (FG) holds. We apply this to prove that if L is a lattice with a nontrivial distributive interval, then L has a proper congruence-preserving extension.
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