پديد آورنده :
سنگ تراشان خدمي، آمنه
عنوان :
مطالعه بعد گلدي حلقه ها و مدول ها
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي محض﴿جبر﴾
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
[هشت]،94،[II]،ص.
يادداشت :
ص.ع.به:فارسي وانگليسي
استاد راهنما :
محمد رضا ودادي
توصيفگر ها :
حلقه هاي موروثي , حلقه هاي نوتري , پوشش شبه تزريقي
تاريخ نمايه سازي :
8/4/88
استاد داور :
منصور معتمدي، عاطفه قرباني
تاريخ ورود اطلاعات :
1396/09/12
چكيده فارسي :
به فارسي و انگليسي:قابل رويت در نسخه ديجيتال
چكيده انگليسي :
On The Goldie Dimension Of Rings and Modules Amene Sangtarashan Khormi ats 1361@math iut ac ir February 4 2009 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Mohammad Reza Vedadi mrvedadi@cc iut ac ir2000 MSC Primary 16D50 Secondary 16D90 Key words Goldie dimension Hereditary rings Noetherian rings Quasi injective hull AbstractIn this thesis we present an expanded account of on the Goldie dimension of rings and mod ules based on an article by Hai Q Dinh Pedro A Guil Asensio Sergio R L pez Permouth o 2006 Let R be an associative ring with identity and M be an unital right R module The in nite Goldie or uniform dimension of a right R module M Gdim M is de ned to bethe supremum of all cardinal numbers such that there exists a direct sum I Mi M ofnon zero submodules of M with I This de nition bring up by J Dauns and L Fuchs 1988 A main question when dealing with in nite Goldie dimensions of modules is whethera module of Goldie dimension must necessarily contain a direct sum non zero submod ules They proved that unless Gdim M is inaccessible cardinals M contains a direct sum ofGdim M non zero submodules Moreover some examples are given showing that this resultis not true in general In this thesis we continue this line of research by studying the Goldie dimension of nonsingu lar modules over hereditary rings First we show that if M is a nitely generated hereditarymodule whose quasi injective hull is generated for some in nite cardinal number then Mcannot contain an independent family of non zero submodules When is not an inacces sible cardinal this means that Gdim M Several consequences are derived from this fact Among them we show that every right hereditary module such that the quasi injective hullsof its cyclic submodules are countably generated is a direct sum of noetherian modules Inparticular we get that every right hereditary ring with countably generated injective hull isright noetherian Possibly the most interesting consequence is where it is shown that everyright hereditary ring with nitely generated injective envelope is right artinian thus answer ing a long standing open question posed by Dung G mez Pardo and Wisbauer 1990 1993 oWe extend our results to modules M over right hereditary rings such that the quasi injectivehull of M is presented for some cardinal number of co nality 0 In particular we obtainthat any countably presented quasi injective module over such a ring is a direct sum of uni form modules We close the paper by discussing possible ways to extend our techniques todeal with a more general question Namely whether any nitely generated module satisfyingthat every quotient is injective is a direct sum of uniforms We also show that our resultsgive partial positive answers to this other conjecture 1
استاد راهنما :
محمد رضا ودادي
استاد داور :
منصور معتمدي، عاطفه قرباني
