Geodesic
Indexed annihilators in lattices
Archivum mathematicum, Tome 31 (1995) no. 4, pp. 259-262 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 
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     author = {Chajda, Ivan},
     title = {Indexed annihilators in lattices},
     journal = {Archivum mathematicum},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1995_31_4_a1/}
}
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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/

[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