Module decompositions via Rickart modules
This work is devoted to the investigation of module decompositions which arise from Rickart modules, socle and radical of modules. In this regard, the structure and several illustrative examples of inverse split modules relative to the socle and radical are given. It is shown that a module \(M\) has...
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Lugansk National Taras Shevchenko University
2018
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admjournalluguniveduua-article-3272018-10-20T08:02:25Z Module decompositions via Rickart modules Harmanci, Abdullah Ungor, Burcu \(\mathrm{Soc}(\cdot)\)-inverse split module, \(\mathrm{Rad}(\cdot)\)-inverse split module, Rickart module 16D10; 16D40; 16D80 This work is devoted to the investigation of module decompositions which arise from Rickart modules, socle and radical of modules. In this regard, the structure and several illustrative examples of inverse split modules relative to the socle and radical are given. It is shown that a module \(M\) has decompositions \(M=\mathrm{Soc}(M) \oplus N\) and \(M=\mathrm{Rad}(M) \oplus K\) where \(N\) and \(K\) are Rickart if and only if \(M\) is \(\mathrm{Soc}(M)\)-inverse split and \(\mathrm{Rad}(M)\)-inverse split, respectively. Right \(\mathrm{Soc}(\cdot)\)-inverse split left perfect rings and semiprimitive right hereditary rings are determined exactly. Also, some characterizations for a ring \(R\) which has a decomposition \(R=\mathrm{Soc}(R_R)\oplus I\) with \(I\) hereditary Rickart module are obtained. Lugansk National Taras Shevchenko University 2018-10-20 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/327 Algebra and Discrete Mathematics; Vol 26, No 1 (2018) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/327/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/327/438 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-10-20T08:02:25Z |
| collection |
OJS |
| language |
English |
| topic |
\(\mathrm{Soc}(\cdot)\)-inverse split module \(\mathrm{Rad}(\cdot)\)-inverse split module Rickart module 16D10 16D40 16D80 |
| spellingShingle |
\(\mathrm{Soc}(\cdot)\)-inverse split module \(\mathrm{Rad}(\cdot)\)-inverse split module Rickart module 16D10 16D40 16D80 Harmanci, Abdullah Ungor, Burcu Module decompositions via Rickart modules |
| topic_facet |
\(\mathrm{Soc}(\cdot)\)-inverse split module \(\mathrm{Rad}(\cdot)\)-inverse split module Rickart module 16D10 16D40 16D80 |
| format |
Article |
| author |
Harmanci, Abdullah Ungor, Burcu |
| author_facet |
Harmanci, Abdullah Ungor, Burcu |
| author_sort |
Harmanci, Abdullah |
| title |
Module decompositions via Rickart modules |
| title_short |
Module decompositions via Rickart modules |
| title_full |
Module decompositions via Rickart modules |
| title_fullStr |
Module decompositions via Rickart modules |
| title_full_unstemmed |
Module decompositions via Rickart modules |
| title_sort |
module decompositions via rickart modules |
| description |
This work is devoted to the investigation of module decompositions which arise from Rickart modules, socle and radical of modules. In this regard, the structure and several illustrative examples of inverse split modules relative to the socle and radical are given. It is shown that a module \(M\) has decompositions \(M=\mathrm{Soc}(M) \oplus N\) and \(M=\mathrm{Rad}(M) \oplus K\) where \(N\) and \(K\) are Rickart if and only if \(M\) is \(\mathrm{Soc}(M)\)-inverse split and \(\mathrm{Rad}(M)\)-inverse split, respectively. Right \(\mathrm{Soc}(\cdot)\)-inverse split left perfect rings and semiprimitive right hereditary rings are determined exactly. Also, some characterizations for a ring \(R\) which has a decomposition \(R=\mathrm{Soc}(R_R)\oplus I\) with \(I\) hereditary Rickart module are obtained. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/327 |
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AT harmanciabdullah moduledecompositionsviarickartmodules AT ungorburcu moduledecompositionsviarickartmodules |
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2025-12-02T15:35:55Z |
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2025-12-02T15:35:55Z |
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1850411325356769280 |