پديد آورنده :
بهبودي، غلامرضا
عنوان :
هم- حلقه هاي هم- ماتريس و دو- مدول ها
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
يادداشت :
ص.ع. به: فارسي و انگليسي
استاد راهنما :
محمد رضا ودادي، بهرام رنگي پور
استاد مشاور :
محمود بهبودي
توصيفگر ها :
مدول هاي جدايي پذير , مدول هاي فروبنيوس , هم- حلقه هاي هم- جدايي پذير , حلقه هاي هم- شكافتني , هم- حلقه فروبنيوس
تاريخ نمايه سازي :
19/11/88
استاد داور :
حسين خبازيان، عاطفه قرباني
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتال
چكيده انگليسي :
On Comatrix Corings and Bimodules Gholamreza Behboodi gh behboodi@math iut ac ir August 12 2009 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisors Dr Mohammad Reza Vedadi mrvedadi@cc iut ac ir and Dr Bahram Rangipour University of New Brunswick Canada bahram@unb ca 2000 MSC 16W30 13B02 Key words separable bimodules frobenius bimodules comatrix corings coseparable corings cosplit cor ings frobenius corings Abstract In this thesis we present an expanded account of on comatrix corings and bimodulesbased on an article by Tomasz Brzezi ski and Jos Gom z Torrecilas 2003 n e eOne of the rst and most fundamental examples of corings is provided by the canonicalcoring of Sweedler which can be associated to any ring extension B A For instance ifB A is an algebra extension then A B A is canonical Sweedler s coring in relation toabove extension The structure of the canonical coring detects whether such an extension isseparable split or frobenius Recently in 13 it has been realized that Sweedler s canonicalcorings are special examples of more general class of corings termed comatrix corings Acomatrix A coring can be associated to any B A bimodule M provided M is a nitelygenerated projective right A module It is natural to expect that such a coring shouldre ect properties of module M in a way similar to the relationship between properties of ringextension and those of corresponding canonical coring Let M be any B A bimodule that is nitely generated and projective right A module and M Hom A M A be a dual of M Then M B M is a comatrix coring in relationto bimodule M The aim of this paper it to study properties of comatrix coring M B Min relation to properties of bimodule M In particular we show that the M is a separablebimodule if and only if the corresponding comatrix coring M B M is a cosplit coring On the other hand if M is a separable resp frobenius bimodule then the comatrix coringM B M is coseparable resp frobenius coring The converse holds provided certain faithful atness condition is satis ed In addition since for any B A bimodule M one can consider a ring extension B S where S is the right endomorphism ring of M there is also associated canonical Sweedler scoring In this thesis we also study how the above properties of a comatrix coring are re ectedby the properties of corresponding Sweedler s coring For example it is shown that if thecomatrix coring M B M is cosplit resp coseparable coring then sweedler s coring S B Sis cosplit resp coseprable coring It is also shown that if the comatrix coring M B M isa frobenius A coring then sweedler s coring S B S is a frobenius S coring 1
استاد راهنما :
محمد رضا ودادي، بهرام رنگي پور
استاد مشاور :
محمود بهبودي
استاد داور :
حسين خبازيان، عاطفه قرباني