On lattices, modules and groups with many uniform elements

On lattices, modules and groups with many uniform elements

The uniform dimension, also known as Goldie dimension, can be defined and used not only in the class of modules, but also in large classes of lattices and groups. For considering this dimension it is necessary to involve uniform elements. In this paper we are going to discuss properties of lattices...

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Date:2018
Main Author: Krempa, Jan
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
Subjects:
uniform element
locally uniform lattice
lattice of subgroups
lattice of submodules
06C99
16S90
20E15
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/981
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id oai:ojs.admjournal.luguniv.edu.ua:article-981
record_format ojs
spelling oai:ojs.admjournal.luguniv.edu.ua:article-9812018-05-14T08:03:48Z On lattices, modules and groups with many uniform elements Krempa, Jan uniform element, locally uniform lattice, lattice of subgroups, lattice of submodules 06C99, 16S90, 20E15 The uniform dimension, also known as Goldie dimension, can be defined and used not only in the class of modules, but also in large classes of lattices and groups. For considering this dimension it is necessary to involve uniform elements. In this paper we are going to discuss properties of lattices with many uniform elements. Further, we examine these properties in the case of lattices of submodules and of subgroups. We also formulate some questions related to the subject of this note. Lugansk National Taras Shevchenko University 2018-05-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/981 Algebra and Discrete Mathematics; Vol 3, No 1 (2004) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/981/510 Copyright (c) 2018 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2018-05-14T08:03:48Z
collection OJS
language English
topic uniform element
locally uniform lattice
lattice of subgroups
lattice of submodules
06C99
16S90
20E15
spellingShingle uniform element
locally uniform lattice
lattice of subgroups
lattice of submodules
06C99
16S90
20E15
Krempa, Jan
On lattices, modules and groups with many uniform elements
topic_facet uniform element
locally uniform lattice
lattice of subgroups
lattice of submodules
06C99
16S90
20E15
format Article
author Krempa, Jan
author_facet Krempa, Jan
author_sort Krempa, Jan
title On lattices, modules and groups with many uniform elements
title_short On lattices, modules and groups with many uniform elements
title_full On lattices, modules and groups with many uniform elements
title_fullStr On lattices, modules and groups with many uniform elements
title_full_unstemmed On lattices, modules and groups with many uniform elements
title_sort on lattices, modules and groups with many uniform elements
description The uniform dimension, also known as Goldie dimension, can be defined and used not only in the class of modules, but also in large classes of lattices and groups. For considering this dimension it is necessary to involve uniform elements. In this paper we are going to discuss properties of lattices with many uniform elements. Further, we examine these properties in the case of lattices of submodules and of subgroups. We also formulate some questions related to the subject of this note.
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/981
work_keys_str_mv AT krempajan onlatticesmodulesandgroupswithmanyuniformelements
first_indexed 2025-07-17T10:36:50Z
last_indexed 2025-07-17T10:36:50Z
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