Indexed annihilators in lattices. (English) Zbl 0860.06005

Chajda, Ivan

Arch. Math., Brno 31, No. 4, 259-262 (1995).

Let \(L\) be a lattice and \(a,b\in L\). An annihilator \(\langle a,b\rangle\) in \(L\) is the set \(\{x\in L: x\wedge a\leq b\}\). The author modifies this definition as follows: Let \(L\) be a lattice, \(\Gamma\neq \emptyset\) an index set and \(a_\gamma, b_\gamma\in L\) for \(\gamma\in \Gamma\). By an indexed annihilator is meant the set \(\{x\in L: a_\gamma\wedge x\leq b_\gamma\) for each \(\gamma\in \Gamma\}\). The author derives some straightforward consequences of this concept.

Reviewer: T.Katriňák (Bratislava)

MSC:

06B10	Lattice ideals, congruence relations
06D15	Pseudocomplemented lattices

Keywords:

indexed annihilator