Indexed annihilators in lattices

Ivan Chajda

Archivum Mathematicum (1995)

  • Volume: 031, Issue: 4, page 259-262
  • ISSN: 0044-8753

Abstract

top
The concept of annihilator in lattice was introduced by M. Mandelker. Although annihilators have some properties common with ideals, the set of all annihilators in L need not be a lattice. We give the concept of indexed annihilator which generalizes it and we show the basic properties of the lattice of indexed annihilators. Moreover, distributive and modular lattices can be characterized by using of indexed annihilators.

How to cite

top

Chajda, Ivan. "Indexed annihilators in lattices." Archivum Mathematicum 031.4 (1995): 259-262. <http://eudml.org/doc/247696>.

@article{Chajda1995,
abstract = {The concept of annihilator in lattice was introduced by M. Mandelker. Although annihilators have some properties common with ideals, the set of all annihilators in $L$ need not be a lattice. We give the concept of indexed annihilator which generalizes it and we show the basic properties of the lattice of indexed annihilators. Moreover, distributive and modular lattices can be characterized by using of indexed annihilators.},
author = {Chajda, Ivan},
journal = {Archivum Mathematicum},
keywords = {lattice; distributive lattice; modular lattice; annihilator; ideal; indexed annihilator; indexed annihilator},
language = {eng},
number = {4},
pages = {259-262},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Indexed annihilators in lattices},
url = {http://eudml.org/doc/247696},
volume = {031},
year = {1995},
}

TY - JOUR
AU - Chajda, Ivan
TI - Indexed annihilators in lattices
JO - Archivum Mathematicum
PY - 1995
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 031
IS - 4
SP - 259
EP - 262
AB - The concept of annihilator in lattice was introduced by M. Mandelker. Although annihilators have some properties common with ideals, the set of all annihilators in $L$ need not be a lattice. We give the concept of indexed annihilator which generalizes it and we show the basic properties of the lattice of indexed annihilators. Moreover, distributive and modular lattices can be characterized by using of indexed annihilators.
LA - eng
KW - lattice; distributive lattice; modular lattice; annihilator; ideal; indexed annihilator; indexed annihilator
UR - http://eudml.org/doc/247696
ER -

References

top
  1. Annihilators in modular lattices, Algebra Univ. 22 (1986), 154-158. (1986) MR0870463
  2. Relative annihilators in lattices, Duke Math. J. 40 (1970), 377-386. (1970) Zbl0206.29701MR0256951

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.