Isomorphic sheaf representations of normal lattices
type: Item
instance of: scholarly article
title: Isomorphic sheaf representations of normal lattices
zbMATH Open document ID: 0646.06009
DOI: 10.1016/0022-4049(87)90071-5
author: George Georgescu
author: Ioana Voiculescu
published in: Journal of Pure and Applied Algebra
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 06D05
Mathematics Subject Classification ID: 18F20
zbMATH DE Number: 4053697
zbMATH Keywords: distributive lattice
zbMATH Keywords: sheaf representaton
zbMATH Keywords: subframe of ideals
zbMATH Keywords: normal lattices
MaRDI profile type: Publication
full work available at URL: 0022-4049(87)90071-5
OpenAlex ID: W2053802811
cites work: Q4083730
cites work: Recovering a frame from its sheaves of algebras
cites work: A Sheaf Representation for Modules with Applications to Gelfand Rings
cites work: Q5574727
cites work: Q4175407
cites work: Normal lattices
cites work: The multiplier extension of a distributive lattice
cites work: Q4161366
cites work: Q3965241
cites work: Q3966191
cites work: Reticulated rings
cites work: Sheaf representations of strongly harmonic rings
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description: scientific article; zbMATH DE number 4053697