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Title: Non-transitive generalizations of subdirect products of linearly ordered rings (English)
Author: Rachůnek, Jiří
Author: Šalounová, Dana
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 53
Issue: 3
Year: 2003
Pages: 591-603
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: weakly associative lattice ring
Keyword: weakly associative lattice group
Keyword: representable wal-ring
MSC: 06F15
MSC: 06F25
MSC: 13J25
MSC: 16W80
idZBL: Zbl 1080.06032
idMR: MR2000055
Date available: 2009-09-24T11:04:43Z
Last updated: 2020-07-03
Stable URL:
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