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Non-transitive generalizations of subdirect products of linearly ordered rings

Jiří Rachůnek, Dana Šalounová (2003)

Czechoslovak Mathematical Journal

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...

On absolute retracts and absolute convex retracts in some classes of l-groups

Ján Jakubík (2003)

Discussiones Mathematicae - General Algebra and Applications

By dealing with absolute retracts of l-groups we use a definition analogous to that applied by Halmos for the case of Boolean algebras. The main results of the present paper concern absolute convex retracts in the class of all archimedean l-groups and in the class of all complete l-groups.

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