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

top
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

top

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

top
  1. Lattice-Ordered Groups (An Introduction), D. Reidel Publishing Company, 1988. (1988) MR0937703
  2. a * -closures of lattice-ordered groups, Trans. Math. Soc. 209 (1975), 367-387. (1975) MR0404087
  3. Lattice-Ordered Groups, Tulane Lecture Notes (1970), Tulane University. (1970) Zbl0258.06011
  4. K -radical classes of lattice ordered groups, Algebra, Proc. Conf. Carbondale (1980), Lecture Notes Math., 848, 186-207. (1980) MR0613186
  5. Closure operators on radical classes of lattice-ordered groups, Czech. Math. J. 37(112) (1987), 51-64. (1987) Zbl0661.06007MR0875127
  6. Lattice-Ordered Groups (Advances and Techniques), Kluwer Academic Publisher, 1989. (1989) MR1036072
  7. Radical mappings and radical classes of lattice ordered groups, Symposia Math. 21 (1977), 451-477, Academic Press. (1977) Zbl0368.06013MR0491397
  8. On K -radical classes of lattice ordered groups, Czech. Math. J. 33(108) (1983), 149-163. (1983) Zbl0521.06016MR0687428
  9. Lattice-Ordered Groups, Ph.D. dissertation, University of Kansas (1975). (1975) MR2625950
  10. Torsion theory for lattice ordered groups, Czech. Math. J. 25(100) (1975), 284-299. (1975) Zbl0321.06020MR0389705
  11. Product radical classes of -groups, Czech. Math. J. 42(117) (1992), 129-142. (1992) MR1152176

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.