پديد آورنده :
بازيار، محمد
عنوان :
مدول هاي نيم درون ساده و مدول هاي تماما كش
گرايش تحصيلي :
جبر ناجابجايي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
نه، 113، [II] ص:-
يادداشت :
ص.ع. به: فارسي و انگليسي
استاد راهنما :
احمد حقاني
استاد مشاور :
محمدرضا ودادي
تاريخ نمايه سازي :
14/12/87
استاد داور :
اميدعلي شهني كرم زاده، حبيب شريف، حسين خبازيان، محمود بهبودي
كد ايرانداك :
ID217 دكتري
چكيده فارسي :
به فارسي و انگليسي: قابل رؤيت در نسخه ديجيتال
چكيده انگليسي :
Semi endosimple Modules and Fully Kasch Modules Mohammad Baziar baziar@math iut ac ir 09 21 2008 Doctor of Philosophy Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Prof Ahmad Haghany aghagh@cc iut ac ir Advisor Dr Mohammad Reza Vedadi mrvedadi@cc iut ac ir Department Graduate Program Coordinator Dr Rasoul Nasr Isfahani isfahani@cc iut ac ir Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran AbstractIn the rst part of the thesis a module is called semi endosimple if it has no proper fully in variant essential submodules Basic property of semi endosimple modules are explored andring with all nitely generated modules semi endosimple are characterized It is proved thata hereditary left Noetherian ring has all nitely generated modules semi endosimple if andonly if it is a nite direct sum of simple Noetherian V rings For quasi projective modules equivalent conditions to semi endosimplicity of their quasi injective hulls are found and newcharacterizations of strongly semiprime rings V rings and Noetherian V rings are establishedin terms of semi endosimplicity of appropriate modules in each case It is shown that theendomorphism ring of a quasi projective retractable module is a nite direct sum of simplerings if and only if the module is nitely generated semi endosimple Finally semisimplicityof a module in connection to semi endosimplicity is investigated and it is proved amongother things that a module M is semisimple if and only if M is semi endosimple and any0 N M has a semiprime endomorphism ring In the second part of the thesis we carry out a study of modules MR satisfying the propertythat every module in M is a Kasch module Such modules are called fully Kasch Sev eral su cient conditions for a module to be fully Kasch are given which are also necessaryin case the module satis es a property named condition We prove that if R is eitherright Artinian or right FBN or Morita equivalent to a right duo ring then every R modulesatis es When R is Morita equivalent to a right duo ring MR is fully Kasch if and onlyif R annR mR is a left perfect ring for any non zero m M These considerations tackle aquestion raised by Albu and Wisbauer Key WordsSemi endosimple Strongly semiprime Fully invariant essential Co retractable Fully Kaschmodule Perfect ring IntroductionAs a simultaneous generalization of weakly primitive rings 21 and strongly prime rings 4 Desale and Nicholson 6 de ned an endoprimitive ring R for which one of several equiva lent de nitions is the existence of a faithful endosimple module where a non zero module iscalled endosimple if it has no non trivial fully invariant submodules With this terminology an endosimple module MR is strongly prime that is M is contained in every non zero fully 1
استاد راهنما :
احمد حقاني
استاد مشاور :
محمدرضا ودادي
استاد داور :
اميدعلي شهني كرم زاده، حبيب شريف، حسين خبازيان، محمود بهبودي
