Axiomatic Definition of Small Cancellation Rings

In the present paper, we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three specific axioms for corresponding defining relations that provide the small cancellation proper...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Doklady. Mathematics 2021-09, Vol.104 (2), p.234-239
Hauptverfasser:	Atkarskaya, A., Kanel-Belov, A., Plotkin, E., Rips, E.
Format:	Artikel
Sprache:	eng
Schlagworte:	Axioms Cancellation Group theory Mathematics Mathematics and Statistics Quotients
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page	239
container_issue	2
container_start_page	234
container_title	Doklady. Mathematics
container_volume	104
creator	Atkarskaya, A. Kanel-Belov, A. Plotkin, E. Rips, E.
description	In the present paper, we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three specific axioms for corresponding defining relations that provide the small cancellation properties of the obtained ring. We show that this ring is nontrivial. It is called a small cancellation ring.
doi_str_mv	10.1134/S1064562421050197
format	Article
fullrecord	<record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2625297118</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2625297118</sourcerecordid><originalsourceid>FETCH-LOGICAL-c198t-48e7d38080ad49a807f62720816d4da5bf28a3a976684720821089342cd875a3</originalsourceid><addsrcrecordid>eNp1UEtLw0AQXkTBWv0B3gKeozP7zrFErUJBsL2HNdmULcmm7qag_96tETyIpxm-1wwfIdcIt4iM360RJBeScoogAAt1QmYoGOaaSXqa9kTnR_6cXMS4A-CCAswILD7c0JvR1dm9bZ13oxt8NrTZujddl5XG17brzDf66vw2XpKz1nTRXv3MOdk8PmzKp3z1snwuF6u8xkKPOddWNUyDBtPwwmhQraSKgkbZ8MaIt5Zqw0yhpNT8iKe_dcE4rRuthGFzcjPF7sPwfrBxrHbDIfh0saKSClooRJ1UOKnqMMQYbFvtg-tN-KwQqmMv1Z9ekodOnpi0fmvDb_L_pi_3KGEg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2625297118</pqid></control><display><type>article</type><title>Axiomatic Definition of Small Cancellation Rings</title><source>SpringerLink Journals - AutoHoldings</source><creator>Atkarskaya, A. ; Kanel-Belov, A. ; Plotkin, E. ; Rips, E.</creator><creatorcontrib>Atkarskaya, A. ; Kanel-Belov, A. ; Plotkin, E. ; Rips, E.</creatorcontrib><description>In the present paper, we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three specific axioms for corresponding defining relations that provide the small cancellation properties of the obtained ring. We show that this ring is nontrivial. It is called a small cancellation ring.</description><identifier>ISSN: 1064-5624</identifier><identifier>EISSN: 1531-8362</identifier><identifier>DOI: 10.1134/S1064562421050197</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Axioms ; Cancellation ; Group theory ; Mathematics ; Mathematics and Statistics ; Quotients</subject><ispartof>Doklady. Mathematics, 2021-09, Vol.104 (2), p.234-239</ispartof><rights>Pleiades Publishing, Ltd. 2021. ISSN 1064-5624, Doklady Mathematics, 2021, Vol. 104, No. 2, pp. 234–239. © Pleiades Publishing, Ltd., 2021. Russian Text © The Author(s), 2021, published in Doklady Rossiiskoi Akademii Nauk. Matematika, Informatika, Protsessy Upravleniya, 2021, Vol. 500, pp. 16–22.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c198t-48e7d38080ad49a807f62720816d4da5bf28a3a976684720821089342cd875a3</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/S1064562421050197$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S1064562421050197$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Atkarskaya, A.</creatorcontrib><creatorcontrib>Kanel-Belov, A.</creatorcontrib><creatorcontrib>Plotkin, E.</creatorcontrib><creatorcontrib>Rips, E.</creatorcontrib><title>Axiomatic Definition of Small Cancellation Rings</title><title>Doklady. Mathematics</title><addtitle>Dokl. Math</addtitle><description>In the present paper, we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three specific axioms for corresponding defining relations that provide the small cancellation properties of the obtained ring. We show that this ring is nontrivial. It is called a small cancellation ring.</description><subject>Axioms</subject><subject>Cancellation</subject><subject>Group theory</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Quotients</subject><issn>1064-5624</issn><issn>1531-8362</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp1UEtLw0AQXkTBWv0B3gKeozP7zrFErUJBsL2HNdmULcmm7qag_96tETyIpxm-1wwfIdcIt4iM360RJBeScoogAAt1QmYoGOaaSXqa9kTnR_6cXMS4A-CCAswILD7c0JvR1dm9bZ13oxt8NrTZujddl5XG17brzDf66vw2XpKz1nTRXv3MOdk8PmzKp3z1snwuF6u8xkKPOddWNUyDBtPwwmhQraSKgkbZ8MaIt5Zqw0yhpNT8iKe_dcE4rRuthGFzcjPF7sPwfrBxrHbDIfh0saKSClooRJ1UOKnqMMQYbFvtg-tN-KwQqmMv1Z9ekodOnpi0fmvDb_L_pi_3KGEg</recordid><startdate>20210901</startdate><enddate>20210901</enddate><creator>Atkarskaya, A.</creator><creator>Kanel-Belov, A.</creator><creator>Plotkin, E.</creator><creator>Rips, E.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20210901</creationdate><title>Axiomatic Definition of Small Cancellation Rings</title><author>Atkarskaya, A. ; Kanel-Belov, A. ; Plotkin, E. ; Rips, E.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c198t-48e7d38080ad49a807f62720816d4da5bf28a3a976684720821089342cd875a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Axioms</topic><topic>Cancellation</topic><topic>Group theory</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Quotients</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Atkarskaya, A.</creatorcontrib><creatorcontrib>Kanel-Belov, A.</creatorcontrib><creatorcontrib>Plotkin, E.</creatorcontrib><creatorcontrib>Rips, E.</creatorcontrib><collection>CrossRef</collection><jtitle>Doklady. Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Atkarskaya, A.</au><au>Kanel-Belov, A.</au><au>Plotkin, E.</au><au>Rips, E.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Axiomatic Definition of Small Cancellation Rings</atitle><jtitle>Doklady. Mathematics</jtitle><stitle>Dokl. Math</stitle><date>2021-09-01</date><risdate>2021</risdate><volume>104</volume><issue>2</issue><spage>234</spage><epage>239</epage><pages>234-239</pages><issn>1064-5624</issn><eissn>1531-8362</eissn><abstract>In the present paper, we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three specific axioms for corresponding defining relations that provide the small cancellation properties of the obtained ring. We show that this ring is nontrivial. It is called a small cancellation ring.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S1064562421050197</doi><tpages>6</tpages></addata></record>
fulltext	fulltext
identifier	ISSN: 1064-5624
ispartof	Doklady. Mathematics, 2021-09, Vol.104 (2), p.234-239
issn	1064-5624 1531-8362
language	eng
recordid	cdi_proquest_journals_2625297118
source	SpringerLink Journals - AutoHoldings
subjects	Axioms Cancellation Group theory Mathematics Mathematics and Statistics Quotients
title	Axiomatic Definition of Small Cancellation Rings
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-06T22%3A28%3A00IST&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=Axiomatic%20Definition%20of%20Small%20Cancellation%20Rings&rft.jtitle=Doklady.%20Mathematics&rft.au=Atkarskaya,%20A.&rft.date=2021-09-01&rft.volume=104&rft.issue=2&rft.spage=234&rft.epage=239&rft.pages=234-239&rft.issn=1064-5624&rft.eissn=1531-8362&rft_id=info:doi/10.1134/S1064562421050197&rft_dat=%3Cproquest_cross%3E2625297118%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=2625297118&rft_id=info:pmid/&rfr_iscdi=true