Some results on abstract commutative ideal theory
type: Item
instance of: scholarly article
title: Some results on abstract commutative ideal theory
zbMATH Open document ID: 0822.06015
DOI: 10.1007/BF01876923
author: Francisco E. Alarcón
author: C. Jayaram
author: D. D. Anderson
published in: Periodica Mathematica Hungarica
publication date: 1995-09-28T00:00:00Z
review text: The authors establish abstract versions of Nakayama's Lemma and the Krull Intersection Theorem. Using these results, they obtain some equivalent conditions for a multiplicative lattice with 1 compact to be a finite Boolean algebra. Further they study multiplicative lattices in which semiprimary elements are primary. They introduce the concepts of weak \(r\)-lattices and weak \(M\)-lattices. They show that a weak \(r\)-lattice is an \(M\)-lattice if and only if it is a weak \(M\)-lattice. Finally they investigate the lattice of filters of a bounded commutative multiplicative semilattice, and using these they characterize regular lattices.
Mathematics Subject Classification ID: 06F99
Mathematics Subject Classification ID: 06E99
zbMATH DE Number: 737237
zbMATH Keywords: Nakayama lemma
zbMATH Keywords: Krull intersection theorem
zbMATH Keywords: multiplicative lattice
zbMATH Keywords: Boolean algebra
zbMATH Keywords: filters
zbMATH Keywords: regular lattices
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01876923
OpenAlex ID: W2056045330
description: scientific article; zbMATH DE number 737237