Characterization of distributive sets by generalized annihilators

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Characterization of distributive sets by generalized annihilators. (English). Archivum Mathematicum, vol. 30 (1994), issue 1, pp. 25-27

MSC: 06A06 | MR 1282110 | Zbl 0805.06001

Keywords:
annihilator; generalized annihilators; ideal; filter

Summary:
Distributive ordered sets are characterized by so called generalized annihilators.

References:

[1] Mandelker, M.: Relative annihilators in lattices. Duke Math. J. 40 (1970), 377-386. MR 0256951 | Zbl 0206.29701

[2] Davey, B.: Some annihilator conditions on distributive lattices. Alg. Universalis 4 (1974), 316-322. MR 0357261 | Zbl 0299.06007

[3] Davey, B., Nieminen, J.: Annihilators in modular lattices. preprint. MR 0870463

[4] Rachůnek, J.: Translations des ensembles ordonnès. Math. Slovaca 31 (1981), 337-340. MR 0637961

[5] Rachůnek, J., Chajda, I.: Forbidden configurations for distributive and modular ordered sets. Order 5 (1989), 407-423. MR 1010389

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