Halaš, Radomír; Chajda, Ivan Indexed annihilators in ordered sets. (English) Zbl 0843.06002 Math. Slovaca 45, No. 5, 501-508 (1995). Summary: The concept of lattice annihilator is modified and generalized for ordered sets as an indexed annihilator. The set of all indexed annihilators \(\text{IA} (S)\) forms a complete lattice. Some properties of \(\text{IA} (S)\) in connection with the lattice of all ideals of \(S\) are studied. Cited in 5 Documents MSC: 06A06 Partial orders, general 06B23 Complete lattices, completions Keywords:distributivity; complete lattice of indexed annihilators; lattice of ideals; ordered sets; indexed annihilator PDF BibTeX XML Cite \textit{R. Halaš} and \textit{I. Chajda}, Math. Slovaca 45, No. 5, 501--508 (1995; Zbl 0843.06002) Full Text: EuDML OpenURL References: [1] CHAJDA I., RACHŮNEK J.: Forbidden configurations for distributive and modular ordered sets. Order 5 (1989), 407-423. · Zbl 0674.06003 [2] DAVEY B.: Some annihilator conditions on distributive lattices. Algebra Universalis 4 (1974), 316-322. · Zbl 0299.06007 [3] DAVEY B., NIEMINEN J.: Annihilators in modular lattices. Algebra Universalis 22 (1986), 154-158. · Zbl 0613.06004 [4] HALAS R.: Characterization of distributive sets by generalized annihilators. Arch. Math. (Brno) 30 (1994), 25-27. · Zbl 0805.06001 [5] MANDELKER M.: Relative annihilators in lattices. Duke Math. J. 40 (1970), 377-386. · Zbl 0206.29701 [6] RACHŮNEK J.: Translations des ensembles ordonnés. Math. Slovaca 31 (1981), 337-340. · Zbl 0472.06002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.