Geodesic
Non-transitive generalizations of subdirect products of linearly ordered rings
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 3, pp. 591-603.

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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.
Classification : 06F15, 06F25, 13J25, 16W80
Keywords: weakly associative lattice ring; weakly associative lattice group; representable wal-ring 
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     title = {Non-transitive generalizations of subdirect products of linearly ordered rings},
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Rachůnek, Jiří; Šalounová, Dana. Non-transitive generalizations of subdirect products of linearly ordered rings. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 3, pp. 591-603. http://geodesic.mathdoc.fr/item/CMJ_2003__53_3_a7/