Non-Transitive Generalizations of Subdirect Products of Linearly Ordered Rings
Jiří Rachůnek, Dana Šalounová · Czechoslovak Mathematical Journal · 2003
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.