Abstract
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.
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Rachůnek, J., Šalounová, D. Non-Transitive Generalizations of Subdirect Products of Linearly Ordered Rings. Czechoslovak Mathematical Journal 53, 591–603 (2003). https://doi.org/10.1023/B:CMAJ.0000024505.21040.c2
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DOI: https://doi.org/10.1023/B:CMAJ.0000024505.21040.c2