A generalization of supplemented modules
Let $M$ be a left module over a ring $R$ and $I$ an ideal of $R$. $M$ is called an $I$-supplemented module (finitely $I$-supplemented module) if for every submodule (finitely generated submodule) $X$ of $M$, there is a submodule $Y$ of $M$ such that $X+Y=M$, $X\cap Y\subseteq IY$ and $X\cap Y$ is PS...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | |
| container_volume | |
| creator | Wang, Yongduo |
| description | Let $M$ be a left module over a ring $R$ and $I$ an ideal of $R$. $M$ is
called an $I$-supplemented module (finitely $I$-supplemented module) if for
every submodule (finitely generated submodule) $X$ of $M$, there is a submodule
$Y$ of $M$ such that $X+Y=M$, $X\cap Y\subseteq IY$ and $X\cap Y$ is PSD in
$Y$. This definition generalizes supplemented modules and $\delta$-supplemented
modules. We characterize $I$-semiregular, $I$-semiperfect and $I$-perfect rings
which are defined by Yousif and Zhou [15] using $I$-supplemented modules. Some
well known results are obtained as corollaries. |
| doi_str_mv | 10.48550/arxiv.1108.3381 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_1108_3381</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1108_3381</sourcerecordid><originalsourceid>FETCH-LOGICAL-a651-5e1f92437f5dd45301bf933e7720f32e6b3110dc3e0d65ae20184b0d8a909dda3</originalsourceid><addsrcrecordid>eNotzj-PgkAQhvFtLIzaW10obcBZhoWlNOROLzGxoSfDzawh4V9AjXefXtGr3u55f0qtNQSRNQa2NNyrW6A12ADR6rna7LyztDJQXf3Rpepar3PeeO37WhppL8Je0_G1lnGpZo7qUVb_u1D512eeHfzjaf-d7Y4-xUb7RrRLwwgTZ5gjg6BLlyJKkoTgMJS4xOc5_6AAx4YkBG2jEthSCikz4UJ9vLMvadEPVUPDbzGJi0mMD4aUOnk</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>A generalization of supplemented modules</title><source>arXiv.org</source><creator>Wang, Yongduo</creator><creatorcontrib>Wang, Yongduo</creatorcontrib><description>Let $M$ be a left module over a ring $R$ and $I$ an ideal of $R$. $M$ is
called an $I$-supplemented module (finitely $I$-supplemented module) if for
every submodule (finitely generated submodule) $X$ of $M$, there is a submodule
$Y$ of $M$ such that $X+Y=M$, $X\cap Y\subseteq IY$ and $X\cap Y$ is PSD in
$Y$. This definition generalizes supplemented modules and $\delta$-supplemented
modules. We characterize $I$-semiregular, $I$-semiperfect and $I$-perfect rings
which are defined by Yousif and Zhou [15] using $I$-supplemented modules. Some
well known results are obtained as corollaries.</description><identifier>DOI: 10.48550/arxiv.1108.3381</identifier><language>eng</language><subject>Mathematics - Rings and Algebras</subject><creationdate>2011-08</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1108.3381$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1108.3381$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Wang, Yongduo</creatorcontrib><title>A generalization of supplemented modules</title><description>Let $M$ be a left module over a ring $R$ and $I$ an ideal of $R$. $M$ is
called an $I$-supplemented module (finitely $I$-supplemented module) if for
every submodule (finitely generated submodule) $X$ of $M$, there is a submodule
$Y$ of $M$ such that $X+Y=M$, $X\cap Y\subseteq IY$ and $X\cap Y$ is PSD in
$Y$. This definition generalizes supplemented modules and $\delta$-supplemented
modules. We characterize $I$-semiregular, $I$-semiperfect and $I$-perfect rings
which are defined by Yousif and Zhou [15] using $I$-supplemented modules. Some
well known results are obtained as corollaries.</description><subject>Mathematics - Rings and Algebras</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzj-PgkAQhvFtLIzaW10obcBZhoWlNOROLzGxoSfDzawh4V9AjXefXtGr3u55f0qtNQSRNQa2NNyrW6A12ADR6rna7LyztDJQXf3Rpepar3PeeO37WhppL8Je0_G1lnGpZo7qUVb_u1D512eeHfzjaf-d7Y4-xUb7RrRLwwgTZ5gjg6BLlyJKkoTgMJS4xOc5_6AAx4YkBG2jEthSCikz4UJ9vLMvadEPVUPDbzGJi0mMD4aUOnk</recordid><startdate>20110816</startdate><enddate>20110816</enddate><creator>Wang, Yongduo</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20110816</creationdate><title>A generalization of supplemented modules</title><author>Wang, Yongduo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a651-5e1f92437f5dd45301bf933e7720f32e6b3110dc3e0d65ae20184b0d8a909dda3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Mathematics - Rings and Algebras</topic><toplevel>online_resources</toplevel><creatorcontrib>Wang, Yongduo</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Wang, Yongduo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A generalization of supplemented modules</atitle><date>2011-08-16</date><risdate>2011</risdate><abstract>Let $M$ be a left module over a ring $R$ and $I$ an ideal of $R$. $M$ is
called an $I$-supplemented module (finitely $I$-supplemented module) if for
every submodule (finitely generated submodule) $X$ of $M$, there is a submodule
$Y$ of $M$ such that $X+Y=M$, $X\cap Y\subseteq IY$ and $X\cap Y$ is PSD in
$Y$. This definition generalizes supplemented modules and $\delta$-supplemented
modules. We characterize $I$-semiregular, $I$-semiperfect and $I$-perfect rings
which are defined by Yousif and Zhou [15] using $I$-supplemented modules. Some
well known results are obtained as corollaries.</abstract><doi>10.48550/arxiv.1108.3381</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.1108.3381 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_1108_3381 |
| source | arXiv.org |
| subjects | Mathematics - Rings and Algebras |
| title | A generalization of supplemented modules |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-19T23%3A00%3A04IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20generalization%20of%20supplemented%20modules&rft.au=Wang,%20Yongduo&rft.date=2011-08-16&rft_id=info:doi/10.48550/arxiv.1108.3381&rft_dat=%3Carxiv_GOX%3E1108_3381%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |