Isomorphic sheaf representations of normal lattices
For a distributive lattice with 0,1 we obtain a sheaf representaton which can be defined on any subframe of ideals of the given lattice. For the case of normal lattices and the subframe of \(\sigma\)-ideals, this sheaf is isomorphic to both sheaves induced on the space of maximal ideals by the Brezuleanu-Diaconescu [\textit{A. Brezuleanu} and \textit{R. Diaconescu}, Rev. Roum. Math. Pures Appl. 14, 311-323 (1969; Zbl 0183.301)] and Cornish [\textit{W. H. Cornish}, ibid. 22, 1059-1067 (1977; Zbl 0382.06011)] representations. As it turns out, the \(\sigma\)-ideals studied by Cornish [loc. cit.] are the lattice-theoretic version of virginal ideals in rings and for normal lattices the situation parallels closely the one for commutative Gelfand rings.
scientific article; zbMATH DE number 4053697
scientific article