Quasi semiprime multiplication modules over a pullback of a pair of Dedekind domains

Quasi semiprime multiplication modules over a pullback of a pair of Dedekind domains

The main purpose of this article is to classify all indecomposable quasi semiprime multiplication modules over pullback rings of two Dedekind domains and establish a connection between the quasi semiprime multiplication modules and the pure-injective modules over such rings. First, we introduce and...

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Bibliographic Details
Date:2023
Main Authors: Ghiasvand, P., Farzalipour, F.
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2023
Subjects:
Dedekind domains
pullback
pure-injective modules
separated modules
quasi semiprime multiplication modules
13C13
13C05
16D70
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1762
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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-1762
record_format ojs
spelling oai:ojs.admjournal.luguniv.edu.ua:article-17622023-03-06T16:39:17Z Quasi semiprime multiplication modules over a pullback of a pair of Dedekind domains Ghiasvand, P. Farzalipour, F. Dedekind domains, pullback, pure-injective modules, separated modules, quasi semiprime multiplication modules 13C13, 13C05, 16D70 The main purpose of this article is to classify all indecomposable quasi semiprime multiplication modules over pullback rings of two Dedekind domains and establish a connection between the quasi semiprime multiplication modules and the pure-injective modules over such rings. First, we introduce and study the notion of quasi semiprime multiplication modules and classify quasi semiprime multiplication modules over local Dedekind domains. Second, we get all indecomposable separated quasi semiprime multiplication modules and then, using this list of separated quasi-semiprime multiplication modules, we show that non-separated indecomposable quasi semiprime multiplication \(R\)-modules with finite-dimensional top are factor modules of finite direct sums of separated indecomposable quasi semiprime multiplication modules. Lugansk National Taras Shevchenko University 2023-03-06 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1762 10.12958/adm1762 Algebra and Discrete Mathematics; Vol 34, No 2 (2022) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1762/pdf Copyright (c) 2023 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2023-03-06T16:39:17Z
collection OJS
language English
topic Dedekind domains
pullback
pure-injective modules
separated modules
quasi semiprime multiplication modules
13C13
13C05
16D70
spellingShingle Dedekind domains
pullback
pure-injective modules
separated modules
quasi semiprime multiplication modules
13C13
13C05
16D70
Ghiasvand, P.
Farzalipour, F.
Quasi semiprime multiplication modules over a pullback of a pair of Dedekind domains
topic_facet Dedekind domains
pullback
pure-injective modules
separated modules
quasi semiprime multiplication modules
13C13
13C05
16D70
format Article
author Ghiasvand, P.
Farzalipour, F.
author_facet Ghiasvand, P.
Farzalipour, F.
author_sort Ghiasvand, P.
title Quasi semiprime multiplication modules over a pullback of a pair of Dedekind domains
title_short Quasi semiprime multiplication modules over a pullback of a pair of Dedekind domains
title_full Quasi semiprime multiplication modules over a pullback of a pair of Dedekind domains
title_fullStr Quasi semiprime multiplication modules over a pullback of a pair of Dedekind domains
title_full_unstemmed Quasi semiprime multiplication modules over a pullback of a pair of Dedekind domains
title_sort quasi semiprime multiplication modules over a pullback of a pair of dedekind domains
description The main purpose of this article is to classify all indecomposable quasi semiprime multiplication modules over pullback rings of two Dedekind domains and establish a connection between the quasi semiprime multiplication modules and the pure-injective modules over such rings. First, we introduce and study the notion of quasi semiprime multiplication modules and classify quasi semiprime multiplication modules over local Dedekind domains. Second, we get all indecomposable separated quasi semiprime multiplication modules and then, using this list of separated quasi-semiprime multiplication modules, we show that non-separated indecomposable quasi semiprime multiplication \(R\)-modules with finite-dimensional top are factor modules of finite direct sums of separated indecomposable quasi semiprime multiplication modules.
publisher Lugansk National Taras Shevchenko University
publishDate 2023
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1762
work_keys_str_mv AT ghiasvandp quasisemiprimemultiplicationmodulesoverapullbackofapairofdedekinddomains
AT farzalipourf quasisemiprimemultiplicationmodulesoverapullbackofapairofdedekinddomains
first_indexed 2025-07-17T10:36:15Z
last_indexed 2025-07-17T10:36:15Z
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