A linear property of Goldie dimension of modules and modular lattices.
type: Item
instance of: scholarly article
title: A linear property of Goldie dimension of modules and modular lattices.
zbMATH Open document ID: 1230.16018
published in: Journal of Pure and Applied Algebra
publication date: 2011-04-29T00:00:00Z
review text: The Goldie dimension is a generalization of the linear dimension of linear spaces. As a basis of a linear space is characterized as a minimal generating subset of the space, the aim of this paper is to study how far this characterization can be extended to the Goldie dimension. In this paper the author studies the Goldie dimension of modular lattices with 0. The author introduces generating subsets of lattices. The main theorems of this paper describe lattices in which minimal generating subsets are bases and those in which the cardinality of every minimal generating subset is equal to the Goldie dimension. Finally, the results on lattices are applied to modules and to the dual Goldie dimension of lattices and modules.
reviewed by: Intan Muchtadi-Alamsyah
Mathematics Subject Classification ID: 16P60
Mathematics Subject Classification ID: 06C05
zbMATH DE Number: 5882444
zbMATH Keywords: Goldie dimension
zbMATH Keywords: modular lattices
zbMATH Keywords: independent sets
zbMATH Keywords: bases
zbMATH Keywords: minimal generating sets
zbMATH Keywords: lattices of submodules
author: E. R. Puczyłowski
MaRDI profile type: Publication
full work available at URL: j.jpaa.2010.09.013
OpenAlex ID: W1966744001
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DOI: 10.1016/J.JPAA.2010.09.013
description: scientific article; zbMATH DE number 5882444