Geodesic
Indexed annihilators in lattices
Archivum mathematicum, Tome 31 (1995) no. 4, pp. 259-262

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MR Zbl
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.
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.
Classification : 06B10, 06C05, 06D05, 06D15
Keywords: lattice; distributive lattice; modular lattice; annihilator; ideal; indexed annihilator 
Chajda, Ivan. Indexed annihilators in lattices. Archivum mathematicum, Tome 31 (1995) no. 4, pp. 259-262. http://geodesic.mathdoc.fr/item/ARM_1995_31_4_a1/
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     title = {Indexed annihilators in lattices},
     journal = {Archivum mathematicum},
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     url = {http://geodesic.mathdoc.fr/item/ARM_1995_31_4_a1/}
}
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[1] Davey, B., Nieminen, J.: Annihilators in modular lattices. Algebra Univ. 22 (1986), 154-158. | MR

[2] Mandelker, M.: Relative annihilators in lattices. Duke Math. J. 40 (1970), 377-386. | MR | Zbl