پديد آورنده :
مصطفي نسب، حجت
عنوان :
مدول ها و هم- مدول هاي هم- اول
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي محض﴿جبر﴾
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
عاطفه قرباني
استاد مشاور :
محمدرضا ودادي
توصيفگر ها :
هم- جبرهاي هم- اول , جبرهاي دوگان
تاريخ نمايه سازي :
16/1/90
استاد داور :
محمود بهبودي،حسين خبازيان
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
On Coprime Modules and Comodules Hojat Mostafanasab h mostafanasab@gmail com 2010 Master of Science Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Atefeh Ghorbani a ghorbani@cc iut ac ir Advisor Dr Mohammad Reza Vedadi mrvedadi@cc iut ac ir 2000 MSC Primery 16W30 Secondary 16D60 Key words Co Prime modules and comodules Coprime coalgebras Dual algebras Abstract From the beginning the study of coalgebras was motivated by the existing theory of algebras and rings Many notions and results could be formulated easily by transferring the corresponding knowledge from algebras to coalgebras and from modules to comodules However despite of its importance in ring theory the notion of primeness for rings and modules did not nd and adequate counterpart in the coalgebraic setting This may be due to the niteness theorem for comodules which says that for a coalgebra C over a eld ring R any nitely generated C comodules is also a nitely generated R modules So to some extent the behaviuor of coalgebras is similar to that of nite dimensional algebras and for those primeness means just simplicity Many observations about coalgebras were inspired by comparable situations for algebras Despite the prominent role of prime algebras the theory of a corresponding notion for coalgebras was not well understood so far Coalgebras C over elds may be called coprime provided the dual algebra C is prime This de nition however is not intrinsic it strongly depends on the base ring being a eld The purpose of the paper is to provide a better understanding of related notions for coalgebras over commutative rings by employing traditional methods from co module theory in particular pre torsion theory Dualising classical primeness condition coprimeness can be de ned for modules and algebras These notions are developed for modules and then applied to comodules We consider prime and coprime fully prime and fully coprime strongly prime and strongly coprime modules and comodules In particular we obtain various characterizations of prime and coprime coalgebras over rings and elds
استاد راهنما :
عاطفه قرباني
استاد مشاور :
محمدرضا ودادي
استاد داور :
محمود بهبودي،حسين خبازيان
