پديد آورنده :
ناظميان، زهرا
عنوان :
بعد تك زنجيري و مباحث مربوطه
گرايش تحصيلي :
رياضي محض، حلقه و مدول
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
عاطفه قرباني
استاد مشاور :
محمود بهبودي
توصيفگر ها :
مدول تك زنجيري , مدول n-زنجيري , مدول نيم ساده , بعد ارزياب , مدول يكنواخت , بعد دوگان زنجيري , حلقه كسر هاي راست ماكسيمال , حلقه ي نيم ساده ي آرتيني
تاريخ نمايه سازي :
94/1/26
استاد داور :
منصور معتمدي،احسان ممتحن،محمد رضا ودادي
كد ايرانداك :
ID735 دكتري
چكيده انگليسي :
Uniserial dimension and related topics Zahra Nazemian z nazemian@math iut ac ir 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Atefeh Ghorbani a ghorbani@cc iut ac ir Advisor Dr Mahmood Behboodi mbehbood@cc iut ac ir 2010 MSC 16D70 16D90 16P70 16A08 03E10 13E05 Keywords Uniserial module Uniserial dimension Semisimple module Valuation dimension Dual uniserial dimension Maximal right quotiont ring AbstractWe de ne and study a new dimension which we call uniserial dimension This ordinal valued dimen sion is a measure of how far a module deviates from being uniserial Noetherian modules are a classof modules with uniserial dimension We characterize rings whose modules have uniserial dimension Uniserial dimension of modules over commutative rings are considered specially We show that theclass of all commutative rings of nite uniserial dimension strictly lies between the class of Artinianrings and the class of semi perfect rings Duality we de ne and study couniserial dimension for mod ules Couniserial dimension is a measure of how far a module deviates from being uniform Eachmodule having such a dimension contains a uniform submodule and every module of nite couniserialdimension has nite uniform dimension Every module of nite length has couniserial dimension andits value lies between the uniform dimension and the length of the module As one of the applications it follows that all right R modules have couniserial dimension if and only if R is a semisimple Artinianring 1 IntroductionThroughout this thesis let R denote an arbitrary ring with identity All modules are assumed to beunitary If N is a submodule resp proper submodule of M we write N M resp N M For amodule MR we write soc M and Rad M for the socle and the Jacobson radical of M respectively
استاد راهنما :
عاطفه قرباني
استاد مشاور :
محمود بهبودي
استاد داور :
منصور معتمدي،احسان ممتحن،محمد رضا ودادي
