On the Schröder-Berstein problem for abelian lattice ordered groups and for MV-algebras (Q1769656)

The author deals with the Schröder-Bernstein property for abelian lattice-ordered groups, proving the following main result: There is a proper class \(C= \{G_i\}_{i\in I}\) of pairwise non-isomorphic abelian lattice-ordered groups satisfying the following three conditions: (a) each \(G_i\) has internal direct factors \(G_1\), and \(G_2\) such that \(G\supset G_1\supset G_2\), \(G\) is isomorphic to \(G_2\), but not to \(G_1\); (b) for all \(i\) and \(j\) in \(I\), \(F(G_i)\) is isomorphic to \(F(G_j)\), where \(F(G)\) is the Boolean algebra of all internal direct factors of \(G\); (c) for each \(i\), \(G_i\) is a vector lattice. The author then proves a similar result for MV-algebras.