Characterizing triplets for modular pseudocomplemented ordered sets (Q2777513)

\textit{T. Katriňák} proved [J. Reine Angew. Math. 241, 160-179 (1970; Zbl 0192.33503)] that every pseudocomplemented distributive lattice \(L\) is determined uniquely up to isomorphism by the so-called characterizing triplet \((B,D,\Phi)\), where \(B=\{x\in L\:|x=x^{**}\}\), \(D=\{y\in L\:|y^{*}=0\}\) and \(\Phi \) is a \(0,1\)-homomorphism of \(L\) into the lattice \(D\) of all filters of \(L\). NEWLINENEWLINENEWLINEIn this paper it is proved that this characterization can be extended to modular pseudocomplemented ordered sets satisfying certain conditions on their ideals, which are trivially valid for lattices but not for ordered sets.