Atoms in lattice of radical classes of lattice-ordered groups

Dao Rong Tong

Archivum Mathematicum (1993)

  • Volume: 029, Issue: 3-4, page 221-226
  • ISSN: 0044-8753

Abstract

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There are several special kinds of radical classes. For example, a product radical class is closed under forming product, a closed-kernel radical class is closed under taking order closures, a K -radical class is closed under taking K -isomorphic images, a polar kernel radical class is closed under taking double polars, etc. The set of all radical classes of the same kind is a complete lattice. In this paper we discuss atoms in these lattices. We prove that every nontrivial element in these lattices has a cover.

How to cite

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Tong, Dao Rong. "Atoms in lattice of radical classes of lattice-ordered groups." Archivum Mathematicum 029.3-4 (1993): 221-226. <http://eudml.org/doc/247441>.

@article{Tong1993,
abstract = {There are several special kinds of radical classes. For example, a product radical class is closed under forming product, a closed-kernel radical class is closed under taking order closures, a $K$-radical class is closed under taking $K$-isomorphic images, a polar kernel radical class is closed under taking double polars, etc. The set of all radical classes of the same kind is a complete lattice. In this paper we discuss atoms in these lattices. We prove that every nontrivial element in these lattices has a cover.},
author = {Tong, Dao Rong},
journal = {Archivum Mathematicum},
keywords = {lattice-ordered group; radical class; closure operator; atom; radical classes; complete lattice; atoms; cover},
language = {eng},
number = {3-4},
pages = {221-226},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Atoms in lattice of radical classes of lattice-ordered groups},
url = {http://eudml.org/doc/247441},
volume = {029},
year = {1993},
}

TY - JOUR
AU - Tong, Dao Rong
TI - Atoms in lattice of radical classes of lattice-ordered groups
JO - Archivum Mathematicum
PY - 1993
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 029
IS - 3-4
SP - 221
EP - 226
AB - There are several special kinds of radical classes. For example, a product radical class is closed under forming product, a closed-kernel radical class is closed under taking order closures, a $K$-radical class is closed under taking $K$-isomorphic images, a polar kernel radical class is closed under taking double polars, etc. The set of all radical classes of the same kind is a complete lattice. In this paper we discuss atoms in these lattices. We prove that every nontrivial element in these lattices has a cover.
LA - eng
KW - lattice-ordered group; radical class; closure operator; atom; radical classes; complete lattice; atoms; cover
UR - http://eudml.org/doc/247441
ER -

References

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  11. Product radical classes of ℓ -groups, Czech. Math. J. 42(117) (1992), 129-142. (1992) MR1152176

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