\(p\)-systems in local Noether lattices
type: Item
instance of: scholarly article
title: \(p\)-systems in local Noether lattices
zbMATH Open document ID: 0812.06008
DOI: 10.1155/S016117129400092X
author: E. W. Johnson
author: Johnny A. Johnson
author: Monty B. Taylor
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1995-04-23T00:00:00Z
full work available at URL: https://eudml.org/doc/47138
review text: Let \(\mathcal L\) be a local Noether lattice, \(M\) its maximal element. The radical of an element \(A \in {\mathcal L}\) is \(\text{Rad}(A) = V\{X \in {\mathcal L}\); \(X^ s \leq A\) for some integer \(s\)\}. If \(Q \in {\mathcal L}\) and \(\text{Rad}(Q) = M\), then the element \(Q\) is called \(M\)-primary. An element \(A \in {\mathcal L}\) which is not of the greatest element of \(\mathcal L\) is a \(p\)-system in \(\mathcal L\) if for every \(M\)-primary element \(Q' \in {\mathcal L}\) such that \(A \leq Q'\) there exists a meet-irreducible \(M\)- primary element \(Q \in {\mathcal L}\) with \(A \leq Q \leq Q'\). The authors give some characterizations of \(p\)-systems in \(\mathcal L\). One of them is topological using a certain metric given on \(\mathcal L\), another one needs the existence of a special decreasing sequence of meet-irreducible \(M\)- primary elements in \(\mathcal L\). Also, \(p\)-systems in quotient lattices and in the metric completion of \(\mathcal L\) are characterized.
Mathematics Subject Classification ID: 06F10
Mathematics Subject Classification ID: 06F05
zbMATH DE Number: 697103
zbMATH Keywords: local Noether lattice
zbMATH Keywords: radical
zbMATH Keywords: \(p\)-system
zbMATH Keywords: \(M\)-primary element
zbMATH Keywords: quotient lattices
zbMATH Keywords: metric completion
reviewed by: Vitězslav Novák
MaRDI profile type: Publication
OpenAlex ID: W2078671990
description: scientific article; zbMATH DE number 697103