Non-Transitive Generalizations of Subdirect Products of Linearly Ordered Rings
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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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- Non-Transitive Generalizations of Subdirect Products of Linearly Ordered Rings
Czechoslovak Mathematical Journal
Volume 53, Issue 3 , pp 591-603
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- weakly associative lattice ring
- weakly associative lattice group
- representable wal-ring
- Author Affiliations
- 1. Department of Algebra and Geometry, Faculty of Sciences, Palacký University, Tomkova 40, 779 00, Olomouc, Czech Republic
- 2. Department of Mathematical Methods in Economy, Faculty of Economics, VŠB–Technical University Ostrava, Sokolská 33, 701 21, Ostrava, Czech Republic