Abelian Groups with Annihilator Ideals of Endomorphism Rings

Abelian Groups with Annihilator Ideals of Endomorphism Rings

We describe the periodic groups whose endomorphism rings satisfy the annihilator condition for the principal left ideals generated by nilpotent elements. We prove that torsion-free reduced separable, vector, and algebraically compact groups have endomorphism rings with the annihilator condition for...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Siberian mathematical journal 2018-03, Vol.59 (2), p.363-367
1. Verfasser: Chekhlov, A. R.
Format: Artikel
Sprache:eng
Schlagworte:
Group theory
Mathematics
Mathematics and Statistics
Rings (mathematics)
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 367
container_issue 2
container_start_page 363
container_title Siberian mathematical journal
container_volume 59
creator Chekhlov, A. R.
description We describe the periodic groups whose endomorphism rings satisfy the annihilator condition for the principal left ideals generated by nilpotent elements. We prove that torsion-free reduced separable, vector, and algebraically compact groups have endomorphism rings with the annihilator condition for the principal left (right) ideals generated by nilpotent elements if and only if these rings are commutative. We show that the almost injective groups (in the sense of Harada) are injective, i.e. divisible.
doi_str_mv 10.1134/S0037446618020192
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2030254918</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2030254918</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-30a95abd1d2a77c9cc6cc7f720b60152638ea8a55732ec369651450c16d6f4413</originalsourceid><addsrcrecordid>eNp1kEtLAzEUhYMoWKs_wF3A9ei9ec0E3JRSq1AQfKyHNJNpU9pkTKaI_94pFVyIq7s43znncgi5RrhF5OLuFYCXQiiFFTBAzU7ICGXJC80UnJLRQS4O-jm5yHkDgABKj8j9ZOm23gQ6T3HfZfrp-zWdhODXfmv6mOhT48w209jSWWjiLqZu7fOOvviwypfkrB1Ed_Vzx-T9YfY2fSwWz_On6WRRWI6qLzgYLc2ywYaZsrTaWmVt2ZYMlgpQMsUrZyojh3eZs1xpJVFIsKga1QqBfExujrldih97l_t6E_cpDJU1Aw5MCo3VQOGRsinmnFxbd8nvTPqqEerDSPWfkQYPO3rywIaVS7_J_5u-AcwjZqo</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2030254918</pqid></control><display><type>article</type><title>Abelian Groups with Annihilator Ideals of Endomorphism Rings</title><source>SpringerLink Journals - AutoHoldings</source><creator>Chekhlov, A. R.</creator><creatorcontrib>Chekhlov, A. R.</creatorcontrib><description>We describe the periodic groups whose endomorphism rings satisfy the annihilator condition for the principal left ideals generated by nilpotent elements. We prove that torsion-free reduced separable, vector, and algebraically compact groups have endomorphism rings with the annihilator condition for the principal left (right) ideals generated by nilpotent elements if and only if these rings are commutative. We show that the almost injective groups (in the sense of Harada) are injective, i.e. divisible.</description><identifier>ISSN: 0037-4466</identifier><identifier>EISSN: 1573-9260</identifier><identifier>DOI: 10.1134/S0037446618020192</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Group theory ; Mathematics ; Mathematics and Statistics ; Rings (mathematics)</subject><ispartof>Siberian mathematical journal, 2018-03, Vol.59 (2), p.363-367</ispartof><rights>Pleiades Publishing, Ltd. 2018</rights><rights>Copyright Springer Science &amp; Business Media 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-30a95abd1d2a77c9cc6cc7f720b60152638ea8a55732ec369651450c16d6f4413</citedby><cites>FETCH-LOGICAL-c316t-30a95abd1d2a77c9cc6cc7f720b60152638ea8a55732ec369651450c16d6f4413</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0037446618020192$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0037446618020192$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Chekhlov, A. R.</creatorcontrib><title>Abelian Groups with Annihilator Ideals of Endomorphism Rings</title><title>Siberian mathematical journal</title><addtitle>Sib Math J</addtitle><description>We describe the periodic groups whose endomorphism rings satisfy the annihilator condition for the principal left ideals generated by nilpotent elements. We prove that torsion-free reduced separable, vector, and algebraically compact groups have endomorphism rings with the annihilator condition for the principal left (right) ideals generated by nilpotent elements if and only if these rings are commutative. We show that the almost injective groups (in the sense of Harada) are injective, i.e. divisible.</description><subject>Group theory</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Rings (mathematics)</subject><issn>0037-4466</issn><issn>1573-9260</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kEtLAzEUhYMoWKs_wF3A9ei9ec0E3JRSq1AQfKyHNJNpU9pkTKaI_94pFVyIq7s43znncgi5RrhF5OLuFYCXQiiFFTBAzU7ICGXJC80UnJLRQS4O-jm5yHkDgABKj8j9ZOm23gQ6T3HfZfrp-zWdhODXfmv6mOhT48w209jSWWjiLqZu7fOOvviwypfkrB1Ed_Vzx-T9YfY2fSwWz_On6WRRWI6qLzgYLc2ywYaZsrTaWmVt2ZYMlgpQMsUrZyojh3eZs1xpJVFIsKga1QqBfExujrldih97l_t6E_cpDJU1Aw5MCo3VQOGRsinmnFxbd8nvTPqqEerDSPWfkQYPO3rywIaVS7_J_5u-AcwjZqo</recordid><startdate>20180301</startdate><enddate>20180301</enddate><creator>Chekhlov, A. R.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20180301</creationdate><title>Abelian Groups with Annihilator Ideals of Endomorphism Rings</title><author>Chekhlov, A. R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-30a95abd1d2a77c9cc6cc7f720b60152638ea8a55732ec369651450c16d6f4413</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Group theory</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Rings (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chekhlov, A. R.</creatorcontrib><collection>CrossRef</collection><jtitle>Siberian mathematical journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chekhlov, A. R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Abelian Groups with Annihilator Ideals of Endomorphism Rings</atitle><jtitle>Siberian mathematical journal</jtitle><stitle>Sib Math J</stitle><date>2018-03-01</date><risdate>2018</risdate><volume>59</volume><issue>2</issue><spage>363</spage><epage>367</epage><pages>363-367</pages><issn>0037-4466</issn><eissn>1573-9260</eissn><abstract>We describe the periodic groups whose endomorphism rings satisfy the annihilator condition for the principal left ideals generated by nilpotent elements. We prove that torsion-free reduced separable, vector, and algebraically compact groups have endomorphism rings with the annihilator condition for the principal left (right) ideals generated by nilpotent elements if and only if these rings are commutative. We show that the almost injective groups (in the sense of Harada) are injective, i.e. divisible.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0037446618020192</doi><tpages>5</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0037-4466
ispartof Siberian mathematical journal, 2018-03, Vol.59 (2), p.363-367
issn 0037-4466
1573-9260
language eng
recordid cdi_proquest_journals_2030254918
source SpringerLink Journals - AutoHoldings
subjects Group theory
Mathematics
Mathematics and Statistics
Rings (mathematics)
title Abelian Groups with Annihilator Ideals of Endomorphism Rings
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-06T09%3A13%3A24IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Abelian%20Groups%20with%20Annihilator%20Ideals%20of%20Endomorphism%20Rings&rft.jtitle=Siberian%20mathematical%20journal&rft.au=Chekhlov,%20A.%20R.&rft.date=2018-03-01&rft.volume=59&rft.issue=2&rft.spage=363&rft.epage=367&rft.pages=363-367&rft.issn=0037-4466&rft.eissn=1573-9260&rft_id=info:doi/10.1134/S0037446618020192&rft_dat=%3Cproquest_cross%3E2030254918%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2030254918&rft_id=info:pmid/&rfr_iscdi=true