Rachůnek, J. & Šalounová, D. Czechoslovak Mathematical Journal (2003) 53: 591. doi:10.1023/B:CMAJ.0000024505.21040.c2
Weakly associative lattice rings (wal-rings) are non-transitive generalizations of lattice ordered rings (l-rings). As is known, the class of l-rings which are subdirect products of linearly ordered rings (i.e. the class of f-rings) plays an important role in the theory of l-rings. In the paper, the classes of wal-rings representable as subdirect products of to-rings and ao-rings (both being non-transitive generalizations of the class of f-rings) are characterized and the class of wal-rings having lattice ordered positive cones is described. Moreover, lexicographic products of weakly associative lattice groups are also studied here.
weakly associative lattice ring weakly associative lattice group representable wal-ring