پديد آورنده :
دهقاني، الهام
عنوان :
حلقه هاي كوته و حلقه هايي كه مدول ها روي آن ها جمع مستقيم مدول هاي توسيعي است
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
ده، 71ص.: مصور، جدول، نمودار
يادداشت :
ص.ع. به فارسي و انگليسي
استاد راهنما :
محمود بهبودي، محمدرضا ودادي
توصيفگر ها :
مدول هاي دوري , حلقه هاي ايدال اصلي , حلقه هاي تك زنجيري , حلقه هاي آرتيني زنجيري
تاريخ نمايه سازي :
24/8/91
استاد داور :
منصوره معتمدي، عاطفه قرباني
تاريخ ورود اطلاعات :
1396/09/21
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
K the Rings and Rings whose Modules o are Direct Sums of Extending Modules Elham Dehghani e dehghani@math iut ac ir 17 09 2012 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mahmood Behboodi m behbood@cc iut ac ir Supervisor Dr Mohammad Reza Vedadi m vedadi@cc iut ac ir 2010 MSC Primmary 16D10 16D70 16P20 Secondary 16N60 16G60 Keywords Cyclic modules K the rings Principal ideal rings Extending module Uniserial rings oArtinian serial ring Ring of nite type Ring of right colocal type Abstract This thesis is based on the works done by M Behboodi A Ghorbani A Moradzadeh S H Shojaeeand Noyan Er see 5 and 12 Let R is an associative ring with identity A left or right K the ring ois a ring R such that each left or right R module is a direct sum of cyclic submodules A ring R iscalled a K the ring if it is both left and right K the ring K the proved that over an Artinian principal o o oideal ring each module is a direct sum of cyclic modules Furthermore if a commutative Artinianring has the property that all its modules are direct sums of cyclic modules then it is necessarilya principal ideal ring Later Cohen and Kaplansky obtained this result that If R is a commutativering such that each R module is a direct sum of cyclic modules then R must be an Artinian principalideal ring Thus by combining results above one obtains that A commutative ring R is a K the ring oif and only if R is an Artinian principal ideal ring First In this thesis we obtain a partial solutionto the question of K the For which rings R is it true that every left or left and right R module is oa direct sum of cyclic modules Let R be a ring in which all idempotents are central for exampleR is duo ring or local ring or uniform ring It is shown that if R is a left K the ring then R is an oArtinian principal right ideal ring Next we conclude that R is K the ring if and only if is an Artinian o
استاد راهنما :
محمود بهبودي، محمدرضا ودادي
استاد داور :
منصوره معتمدي، عاطفه قرباني
