Non-transitive generalizations of subdirect products of linearly ordered rings

Jiří Rachůnek; Dana Šalounová

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 3, page 591-603
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Rachůnek, Jiří, and Šalounová, Dana. "Non-transitive generalizations of subdirect products of linearly ordered rings." Czechoslovak Mathematical Journal 53.3 (2003): 591-603. <http://eudml.org/doc/30801>.

@article{Rachůnek2003,
abstract = {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.},
author = {Rachůnek, Jiří, Šalounová, Dana},
journal = {Czechoslovak Mathematical Journal},
keywords = {weakly associative lattice ring; weakly associative lattice group; representable wal-ring; weakly associative lattice ring; weakly associative lattice group; representable -ring},
language = {eng},
number = {3},
pages = {591-603},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Non-transitive generalizations of subdirect products of linearly ordered rings},
url = {http://eudml.org/doc/30801},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Rachůnek, Jiří
AU - Šalounová, Dana
TI - Non-transitive generalizations of subdirect products of linearly ordered rings
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 3
SP - 591
EP - 603
AB - 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.
LA - eng
KW - weakly associative lattice ring; weakly associative lattice group; representable wal-ring; weakly associative lattice ring; weakly associative lattice group; representable -ring
UR - http://eudml.org/doc/30801
ER -

References

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