توصيفگر ها :
مدول تك-زنجيري , حلقه تك-زنجيري , مدول زنجيري , حلقه زنجيري , مدول ساده مجازي , مدول (homo -)تك-زنجيري مجازي , حلقه (homo -)تك-زنجيري مجازي , مدول (homo -)زنجيري مجازي , حلقه (homo -)زنجيري مجازي , حلقه كوته , FGC-حلقه چپ , FGC-حلقه
چكيده انگليسي :
Virtually Serial Rings and Modules Mohammad Qourchi Nejadi m qourchi@math iut ac ir August 2020 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mahmood Behboodi mbehbood@cc iut ac ir Advisor Dr Ali Moradzadeh Dehkordi a moradzadeh@shahreza ac ir 2010 MSC 16D70 16D60 13A18 13F30 13C99 Keywords Uniserial module serial module homo uniserial module homo serial module virtuallysimple module virtually uniserial module virtually serial module virtually homo uniserial module virtually homo serial module K the ring left FGC ring FGC ring AbstractA theorem due to Nakayama and Skornyakov states that a ring R is an Artinian serial ring if andonly if all left right R modules are serial and two theorem due to Warfield state that a Noetherianring R is serial if and only if every finitely generated left R module is serial and a ring R is leftserial if and only if every finitely generated projective left R module is serial Also a theoremdue to Tuganbaev states that a ring R is a finite direct product of uniserial Noetherian rings if andonly if R is left duo and all injective left R modules are serial and a theorem due to Eisenbud andGriffith states that for a ring R all left R modules are homo serial if and only if R is an Artinianprincipal ideal ring We say that an R module M is virtually uniserial if for every finitely generatedsubmodule 0 K M K Rad K is virtually simple an R module M is virtually simple if M 0and M N for every non zero submodule N of M An R module M is called virtually serial if it is a direct sum of virtually uniserial modules An R module M is virtually homo uniserial if forany finitely generated submodules 0 K L M the factor modules K Rad K and L Rad L arevirtually simple and isomorphic An R module M is called virtually homo serial if it is a direct sumof virtually homo uniserial modules Therefore two interesting natural questions of this sort are Which rings have the property thatevery module proper ideal is virtually homo serial and Which rings have the property thatevery finitely generated module is virtually homo serial Also the above results of Warfield and
