Modules close to SSP- and SIP-modules
In this paper, we investigate some properties of SIP, SSP and CS-Rickart modules. We give equivalent conditions for SIP and SSP modules; establish connections between the class of semisimple artinian rings and the class of SIP rings. It shows that R is a semisimple artinian ring if and only if RR is...
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| Veröffentlicht in: | Lobachevskii journal of mathematics 2017, Vol.38 (1), p.16-23 |
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| container_title | Lobachevskii journal of mathematics |
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| creator | Abyzov, A. N. Nhan, Tran Hoai Ngoc Quynh, Truong Cong |
| description | In this paper, we investigate some properties of SIP, SSP and CS-Rickart modules. We give equivalent conditions for SIP and SSP modules; establish connections between the class of semisimple artinian rings and the class of SIP rings. It shows that
R
is a semisimple artinian ring if and only if RR is SIP and every right R-module has a SIP-cover. We also prove that
R
is a semiregular ring and
J
(
R
) =
Z
(
R
R
) if only if every finitely generated projective module is a CSRickart module which is also a
C
2 module. |
| doi_str_mv | 10.1134/S1995080217010024 |
| format | Article |
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R
is a semisimple artinian ring if and only if RR is SIP and every right R-module has a SIP-cover. We also prove that
R
is a semiregular ring and
J
(
R
) =
Z
(
R
R
) if only if every finitely generated projective module is a CSRickart module which is also a
C
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R
is a semisimple artinian ring if and only if RR is SIP and every right R-module has a SIP-cover. We also prove that
R
is a semiregular ring and
J
(
R
) =
Z
(
R
R
) if only if every finitely generated projective module is a CSRickart module which is also a
C
2 module.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Geometry</subject><subject>Mathematical Logic and Foundations</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Modules</subject><subject>Probability Theory and Stochastic Processes</subject><issn>1995-0802</issn><issn>1818-9962</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kE9LxDAQxYMouK5-AG8F8RjNJG06Ocrin4UVF6rnkKaJuHSbNeke_PZmqQdBPM0w7_fewCPkEtgNgChvG1CqYsg41AwY4-URmQECUqUkP857lulBPyVnKW0ywaWUM3L9HLp971Jh-5BcMYaiada0MENXNMs13U7qOTnxpk_u4mfOydvD_eviia5eHpeLuxW1olIj5U55LqwEo1oh0CP3onLWge9EV0lbGtGysvNKWcQWMF-Nqbnz3kgDyog5uZpydzF87l0a9Sbs45BfakBktUQElSmYKBtDStF5vYsfWxO_NDB9aEP_aSN7-ORJmR3eXfyV_K_pG_mgXvQ</recordid><startdate>2017</startdate><enddate>2017</enddate><creator>Abyzov, A. N.</creator><creator>Nhan, Tran Hoai Ngoc</creator><creator>Quynh, Truong Cong</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2017</creationdate><title>Modules close to SSP- and SIP-modules</title><author>Abyzov, A. N. ; Nhan, Tran Hoai Ngoc ; Quynh, Truong Cong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c359t-2e9f23c61a9b338f82f35ece1fd3d56c4a3b04df99c88b18d3daa72effa6a19a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Geometry</topic><topic>Mathematical Logic and Foundations</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Modules</topic><topic>Probability Theory and Stochastic Processes</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Abyzov, A. N.</creatorcontrib><creatorcontrib>Nhan, Tran Hoai Ngoc</creatorcontrib><creatorcontrib>Quynh, Truong Cong</creatorcontrib><collection>CrossRef</collection><jtitle>Lobachevskii journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Abyzov, A. N.</au><au>Nhan, Tran Hoai Ngoc</au><au>Quynh, Truong Cong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Modules close to SSP- and SIP-modules</atitle><jtitle>Lobachevskii journal of mathematics</jtitle><stitle>Lobachevskii J Math</stitle><date>2017</date><risdate>2017</risdate><volume>38</volume><issue>1</issue><spage>16</spage><epage>23</epage><pages>16-23</pages><issn>1995-0802</issn><eissn>1818-9962</eissn><abstract>In this paper, we investigate some properties of SIP, SSP and CS-Rickart modules. We give equivalent conditions for SIP and SSP modules; establish connections between the class of semisimple artinian rings and the class of SIP rings. It shows that
R
is a semisimple artinian ring if and only if RR is SIP and every right R-module has a SIP-cover. We also prove that
R
is a semiregular ring and
J
(
R
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Z
(
R
R
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C
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| language | eng |
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| subjects | Algebra Analysis Geometry Mathematical Logic and Foundations Mathematics Mathematics and Statistics Modules Probability Theory and Stochastic Processes |
| title | Modules close to SSP- and SIP-modules |
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