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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