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 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
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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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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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| ISSN: | 1726-3255 |