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Algebra and Discrete Mathematics, 2018, том 26, выпуск 1, страницы 47–64
(Mi adm669)
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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
RESEARCH ARTICLE
Module decompositions via Rickart modules
A. Harmancia, B. Ungorb a Department of Mathematics, Hacettepe University, Turkey
b Department of Mathematics, Ankara University, Turkey
Аннотация:
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 $M=\operatorname{Soc}(M) \oplus N$ and $M=\operatorname{Rad}(M) \oplus K$ where $N$ and $K$ are Rickart if and only if $M$ is $\operatorname{Soc}(M)$-inverse split and $\operatorname{Rad}(M)$-inverse split, respectively. Right $\operatorname{Soc}(\,\cdot\,)$-inverse split left perfect rings and semiprimitive right hereditary rings are determined exactly. Also, some characterizations for a ring $R$ which has a decomposition $R=\operatorname{Soc}(R_R)\oplus I$ with $I$ a hereditary Rickart module are obtained.
Ключевые слова:
$\operatorname{Soc}(\,\cdot\,)$-inverse split module, $\operatorname{Rad}(\,\cdot\,)$-inverse split module, Rickart module.
Поступила в редакцию: 22.10.2016 Исправленный вариант: 15.12.2017
Образец цитирования:
A. Harmanci, B. Ungor, “Module decompositions via Rickart modules”, Algebra Discrete Math., 26:1 (2018), 47–64
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm669 https://www.mathnet.ru/rus/adm/v26/i1/p47
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Страница аннотации: | 110 | PDF полного текста: | 44 | Список литературы: | 20 |
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