The Structure of Balanced Rings | Zendy

Dlab Vlastimil | Zendy; Ringel Claus Michael | Zendy

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The Structure of Balanced Rings

Author(s) -

Dlab Vlastimil,

Ringel Claus Michael

Publication year - 1973

Publication title -

proceedings of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.899

H-Index - 65

eISSN - 1460-244X

pISSN - 0024-6115

DOI - 10.1112/plms/s3-26.3.446

Subject(s) - citation , library science , sociology , political science , computer science

Thepresentpaperprovidesacompletedescriptionofleftbalancedrings.Recallthataringiscalledleftbalancedi feveryleft.RmoduleMisbalanced,i.e.if,foranylefti2moduleM,thenaturalhomomorphismofRtothedoublecentralizerofMissurjective.In[4],leftbalancedringshavebeenshowntobeleftartinian.Hence,by[7],aringisleftbalancedifandonlyifi tisa finiteproductoffullmatrixringsoverlocalleftbalancedleftartinianrings.Consequently,thestudyofleftbalancedringsi sreduce dt otha tofleftartinianlocalrings .Throughouttherestofthepaper,Rdenotesalocalleftartinianring,Wisitsradical,andQ= R/W istheresiduedivisionring.ThereisauniquesimpleleftjRmodule

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