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 dec...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/188373 |
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| Zitieren: | Module decompositions via Rickart modules/ A. Harmanci, B. Ungor // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 1. — С. 47–64. — Бібліогр.: 15 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862567827394789376 |
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| author | Harmanci, A. Ungor, B. |
| author_facet | Harmanci, A. Ungor, B. |
| citation_txt | Module decompositions via Rickart modules/ A. Harmanci, B. Ungor // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 1. — С. 47–64. — Бібліогр.: 15 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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 = Soc(M) ⊕ N and M = Rad(M) ⊕ K where N and K are Rickart if and only if M is Soc(M)-inverse split and Rad(M)-inverse split, respectively. Right Soc(·)-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 = Soc(RR) ⊕ I with I a hereditary Rickart module are obtained.
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| first_indexed | 2025-11-26T00:41:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188373 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-26T00:41:48Z |
| publishDate | 2018 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Harmanci, A. Ungor, B. 2023-02-26T12:20:21Z 2023-02-26T12:20:21Z 2018 Module decompositions via Rickart modules/ A. Harmanci, B. Ungor // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 1. — С. 47–64. — Бібліогр.: 15 назв. — англ. 1726-3255 2010 MSC: 16D10, 16D40, 16D80. https://nasplib.isofts.kiev.ua/handle/123456789/188373 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 = Soc(M) ⊕ N and M = Rad(M) ⊕ K where N and K are Rickart if and only if M is Soc(M)-inverse split and Rad(M)-inverse split, respectively. Right Soc(·)-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 = Soc(RR) ⊕ I with I a hereditary Rickart module are obtained. The authors are very thankful to the referee for his/her helpful suggestions to improve the presentation of this paper. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Module decompositions via Rickart modules Article published earlier |
| spellingShingle | Module decompositions via Rickart modules Harmanci, A. Ungor, B. |
| title | 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_short | Module decompositions via Rickart modules |
| title_sort | module decompositions via rickart modules |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188373 |
| work_keys_str_mv | AT harmancia moduledecompositionsviarickartmodules AT ungorb moduledecompositionsviarickartmodules |