Multiplicative lattices and frames
type: Item
instance of: scholarly article
title: Multiplicative lattices and frames
zbMATH Open document ID: 0623.06006
DOI: 10.1007/BF01951002
published in: Acta Mathematica Hungarica
publication date: 1987-01-01T00:00:00Z
review text: The author considers multiplicative lattices, that is complete lattices equipped with an associative binary operation which is distributive over arbitrary joins. As is well known, frames are the special case of multiplicative lattices in which the multiplication is idempotent and has the top element of the lattice as a two-sided unit. Recently there has been some interest in studying certain non-commutative multiplicative lattices (christened quantales by C. J. Mulvey) as a non-commutative generalization of frames, but the present paper is concerned mainly with the commutative case. The main result is an extension to multiplicative lattices whose underlying lattice is continuous of a classical result of W. Krull concerning ideal lattices of commutative rings.
Mathematics Subject Classification ID: 06F05
Mathematics Subject Classification ID: 06B35
Mathematics Subject Classification ID: 06B10
zbMATH DE Number: 4010578
zbMATH Keywords: multiplicative lattices
zbMATH Keywords: complete lattices
zbMATH Keywords: frames
zbMATH Keywords: ideal lattices
author: Jiří Rosický
reviewed by: Peter Johnstone
MaRDI profile type: Publication
cites work: Abstract commutative ideal theory without chain condition
cites work: Theory of \(x\)-ideals
cites work: Q5509706
cites work: Q3898534
cites work: An extension of the Galois theory of Grothendieck
cites work: A unified theory of minimal prime ideals
full work available at URL: https://doi.org/10.1007/bf01951002
OpenAlex ID: W2104663166
description: scientific article; zbMATH DE number 4010578