Indexed annihilators in ordered sets. (English) Zbl 0843.06002

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.


06A06 Partial orders, general
06B23 Complete lattices, completions
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