On a problem of G. Birkhoff
Tadasi Nakayama, Junji Hashimoto · Proceedings of the American Mathematical Society · 1950
In his book Lattice theory, G. Birkhoff proposed to prove that the representation of a finite partially ordered system as the product of indecomposable factors is unique within pairwise isomorphism of factors.' The present short note is to show that this is not the case in general. A simple counterexample, and indeed one of the simplest, perhaps, can be constructed as follows: Let X be the lattice I 0, 1 } of two elements 0, 1 (0 < 1), for instance, and A be the partially ordered system