پديد آورنده :
بهاءلو، مليحه
عنوان :
مدول هاي پايدار و قضيه اي از كاميلو و يو
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
استاد راهنما :
عاطفه قرباني
استاد مشاور :
محمدرضا ودادي
واژه نامه :
به فارسي و انگليسي
توصيفگر ها :
برد پايدار يك , زمينه هاي موريتا , خاصيت تبادلي متناهي , عناصر منظم , عناصر منظم - يكه , خاصيت حذف پذيري داخلي
استاد داور :
احمد حقاني، محمود بهبودي
تاريخ ورود اطلاعات :
1395/01/15
چكيده انگليسي :
Stable modules and a theorem of Camillo and Yu Malihe bahalu m bahaluhoreh@math iut ac ir 2015 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 16E50 16U99 Keywords stable range 1 stable modules Morita contexts internal cancellation Abstract This M Sc thesis is based on the following paperHuanyin Chen and W Keith Nicholson Stable modules and a theorem of Camillo and Yu Journalof Pure and Applied Algebra 218 1431 1442 2014 Throughout this review of thesis we assume that a ring R is associative with an identity andmodules are left modules unless otherwise speci ed Following Bass a ring R has stable range 1 ifra b 1 in R implies that a tb is a unit for some t R equivalently ar b 1 imples a tb is aunit for some t R we extend this equivalence to an arbitrary module and use it to de ne what wemean by a stable module The proof that the stable range condition is right left symmetric is due toVaserstein We begin with a far reaching generalization of Vaserstein s lemma to an arbitrary Moritacontext This engenders the notion of a stable Morita context These contexts are studied and extendmany properties of rings with stable range1 Then all this is applied to the standard context ofa module to de ne and investigate stable modules These are a natural generalization of the stablerange condition for a ring in fact a ring R has stable range 1 if and only if R R is a stable module Ithas been shown that every direct summand of a stable module need not be stable and in this thesis we consider this question Is the direct sum of two stable modules again stable is called regular if m m m for some Hom M R and M An element m in a module RMis called a regular module if every element is regular We extend these notions to an arbitrary Moritacontext A module M is said to have internal cancellation IC if whenever M has two submoduledecompositions M K N L N such that N N then K L Ehrlich proved the following
استاد راهنما :
عاطفه قرباني
استاد مشاور :
محمدرضا ودادي
استاد داور :
احمد حقاني، محمود بهبودي
