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.
@article{107546,
author = {Ivan Chajda},
title = {Indexed annihilators in lattices},
journal = {Archivum Mathematicum},
volume = {031},
year = {1995},
pages = {259-262},
zbl = {0860.06005},
mrnumber = {1390584},
language = {en},
url = {http://dml.mathdoc.fr/item/107546}
}
Chajda, Ivan. Indexed annihilators in lattices. Archivum Mathematicum, Tome 031 (1995) pp. 259-262. http://gdmltest.u-ga.fr/item/107546/
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