Czechoslovak Mathematical Journal

, Volume 53, Issue 3, pp 591–603

Non-Transitive Generalizations of Subdirect Products of Linearly Ordered Rings

  • Jiří Rachůnek
  • Dana Šalounová

DOI: 10.1023/B:CMAJ.0000024505.21040.c2

Cite this article as:
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 

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2003

Authors and Affiliations

  • Jiří Rachůnek
    • 1
  • Dana Šalounová
    • 2
  1. 1.Department of Algebra and GeometryFaculty of Sciences, Palacký University, Tomkova 40OlomoucCzech Republic
  2. 2.Department of Mathematical Methods in EconomyFaculty of Economics, VŠB–Technical University Ostrava, Sokolská 33OstravaCzech Republic

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