1. Non-transitive generalizations of subdirect products of linearly ordered rings
- Creator:
- Rachůnek, Jiří and Šalounová, Dana
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- weakly associative lattice ring, weakly associative lattice group, and representable wal-ring
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public