Group Gradings on Full Matrix Rings
We study G-gradings of the matrix ring Mn(k), k a field, and give a complete description of the gradings where all the elements ei,j are homogeneous, called good gradings. Among these, we determine the ones that are strong gradings or crossed products. If G is a finite cyclic group and k contains a...
Gespeichert in:
| Veröffentlicht in: | Journal of algebra 1999-10, Vol.220 (2), p.709-728 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 728 |
|---|---|
| container_issue | 2 |
| container_start_page | 709 |
| container_title | Journal of algebra |
| container_volume | 220 |
| creator | Dăscălescu, S. Ion, B. Năstăsescu, C. Montes, J.Rios |
| description | We study G-gradings of the matrix ring Mn(k), k a field, and give a complete description of the gradings where all the elements ei,j are homogeneous, called good gradings. Among these, we determine the ones that are strong gradings or crossed products. If G is a finite cyclic group and k contains a primitive |G|th root of 1, we show how all G-gradings of Mn(k) can be produced. In particular we give a precise description of all C2-gradings of M2(k) and show that for algebraically closed k, any such grading is isomorphic to one of the two good gradings. |
| doi_str_mv | 10.1006/jabr.1999.7897 |
| format | Article |
| fullrecord | <record><control><sourceid>elsevier_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1006_jabr_1999_7897</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0021869399978973</els_id><sourcerecordid>S0021869399978973</sourcerecordid><originalsourceid>FETCH-LOGICAL-c326t-ea9844585629e0686edeb4a3ac86afd6cdad0fb5de5ac184adda651b65b42bbb3</originalsourceid><addsrcrecordid>eNp1j01LxDAURYMoWEe3rguuW1_a5k2ylMGpwoggCu7Cy0clQ22HpCP6750ybl1duHAu9zB2zaHkAHi7JRNLrpQql1ItT1jGQUFRIb6fsgyg4oVEVZ-zi5S2AJyLRmbspo3jfpe3kVwYPlI-Dvl63_f5E00xfOcvc3nJzjrqk7_6ywV7W9-_rh6KzXP7uLrbFLaucCo8Kdk0QgqslAeU6J03DdVkJVLn0Dpy0BnhvCDLZUPOEQpuUJimMsbUC1Yed20cU4q-07sYPin-aA56VtSzop4V9ax4AOQR8IdXX8FHnWzwg_UuRG8n7cbwH_oL_QNYQQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Group Gradings on Full Matrix Rings</title><source>Elsevier ScienceDirect Journals Complete</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><creator>Dăscălescu, S. ; Ion, B. ; Năstăsescu, C. ; Montes, J.Rios</creator><creatorcontrib>Dăscălescu, S. ; Ion, B. ; Năstăsescu, C. ; Montes, J.Rios</creatorcontrib><description>We study G-gradings of the matrix ring Mn(k), k a field, and give a complete description of the gradings where all the elements ei,j are homogeneous, called good gradings. Among these, we determine the ones that are strong gradings or crossed products. If G is a finite cyclic group and k contains a primitive |G|th root of 1, we show how all G-gradings of Mn(k) can be produced. In particular we give a precise description of all C2-gradings of M2(k) and show that for algebraically closed k, any such grading is isomorphic to one of the two good gradings.</description><identifier>ISSN: 0021-8693</identifier><identifier>EISSN: 1090-266X</identifier><identifier>DOI: 10.1006/jabr.1999.7897</identifier><language>eng</language><publisher>Elsevier Inc</publisher><ispartof>Journal of algebra, 1999-10, Vol.220 (2), p.709-728</ispartof><rights>1999 Academic Press</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c326t-ea9844585629e0686edeb4a3ac86afd6cdad0fb5de5ac184adda651b65b42bbb3</citedby><cites>FETCH-LOGICAL-c326t-ea9844585629e0686edeb4a3ac86afd6cdad0fb5de5ac184adda651b65b42bbb3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0021869399978973$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids></links><search><creatorcontrib>Dăscălescu, S.</creatorcontrib><creatorcontrib>Ion, B.</creatorcontrib><creatorcontrib>Năstăsescu, C.</creatorcontrib><creatorcontrib>Montes, J.Rios</creatorcontrib><title>Group Gradings on Full Matrix Rings</title><title>Journal of algebra</title><description>We study G-gradings of the matrix ring Mn(k), k a field, and give a complete description of the gradings where all the elements ei,j are homogeneous, called good gradings. Among these, we determine the ones that are strong gradings or crossed products. If G is a finite cyclic group and k contains a primitive |G|th root of 1, we show how all G-gradings of Mn(k) can be produced. In particular we give a precise description of all C2-gradings of M2(k) and show that for algebraically closed k, any such grading is isomorphic to one of the two good gradings.</description><issn>0021-8693</issn><issn>1090-266X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1999</creationdate><recordtype>article</recordtype><recordid>eNp1j01LxDAURYMoWEe3rguuW1_a5k2ylMGpwoggCu7Cy0clQ22HpCP6750ybl1duHAu9zB2zaHkAHi7JRNLrpQql1ItT1jGQUFRIb6fsgyg4oVEVZ-zi5S2AJyLRmbspo3jfpe3kVwYPlI-Dvl63_f5E00xfOcvc3nJzjrqk7_6ywV7W9-_rh6KzXP7uLrbFLaucCo8Kdk0QgqslAeU6J03DdVkJVLn0Dpy0BnhvCDLZUPOEQpuUJimMsbUC1Yed20cU4q-07sYPin-aA56VtSzop4V9ax4AOQR8IdXX8FHnWzwg_UuRG8n7cbwH_oL_QNYQQ</recordid><startdate>19991015</startdate><enddate>19991015</enddate><creator>Dăscălescu, S.</creator><creator>Ion, B.</creator><creator>Năstăsescu, C.</creator><creator>Montes, J.Rios</creator><general>Elsevier Inc</general><scope>6I.</scope><scope>AAFTH</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19991015</creationdate><title>Group Gradings on Full Matrix Rings</title><author>Dăscălescu, S. ; Ion, B. ; Năstăsescu, C. ; Montes, J.Rios</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c326t-ea9844585629e0686edeb4a3ac86afd6cdad0fb5de5ac184adda651b65b42bbb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1999</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dăscălescu, S.</creatorcontrib><creatorcontrib>Ion, B.</creatorcontrib><creatorcontrib>Năstăsescu, C.</creatorcontrib><creatorcontrib>Montes, J.Rios</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>CrossRef</collection><jtitle>Journal of algebra</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dăscălescu, S.</au><au>Ion, B.</au><au>Năstăsescu, C.</au><au>Montes, J.Rios</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Group Gradings on Full Matrix Rings</atitle><jtitle>Journal of algebra</jtitle><date>1999-10-15</date><risdate>1999</risdate><volume>220</volume><issue>2</issue><spage>709</spage><epage>728</epage><pages>709-728</pages><issn>0021-8693</issn><eissn>1090-266X</eissn><abstract>We study G-gradings of the matrix ring Mn(k), k a field, and give a complete description of the gradings where all the elements ei,j are homogeneous, called good gradings. Among these, we determine the ones that are strong gradings or crossed products. If G is a finite cyclic group and k contains a primitive |G|th root of 1, we show how all G-gradings of Mn(k) can be produced. In particular we give a precise description of all C2-gradings of M2(k) and show that for algebraically closed k, any such grading is isomorphic to one of the two good gradings.</abstract><pub>Elsevier Inc</pub><doi>10.1006/jabr.1999.7897</doi><tpages>20</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0021-8693 |
| ispartof | Journal of algebra, 1999-10, Vol.220 (2), p.709-728 |
| issn | 0021-8693 1090-266X |
| language | eng |
| recordid | cdi_crossref_primary_10_1006_jabr_1999_7897 |
| source | Elsevier ScienceDirect Journals Complete; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| title | Group Gradings on Full Matrix Rings |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-13T05%3A14%3A16IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-elsevier_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Group%20Gradings%20on%20Full%20Matrix%20Rings&rft.jtitle=Journal%20of%20algebra&rft.au=D%C4%83sc%C4%83lescu,%20S.&rft.date=1999-10-15&rft.volume=220&rft.issue=2&rft.spage=709&rft.epage=728&rft.pages=709-728&rft.issn=0021-8693&rft.eissn=1090-266X&rft_id=info:doi/10.1006/jabr.1999.7897&rft_dat=%3Celsevier_cross%3ES0021869399978973%3C/elsevier_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_els_id=S0021869399978973&rfr_iscdi=true |