پديد آورنده :
عربي كاكاوند،مرضيه
عنوان :
مدول هاي تقريبا تزريقي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده كشاورزي
يادداشت :
ص.ع.به فارسي وانگليسي
استاد راهنما :
حسين خبازيان
توصيفگر ها :
مدول ساده - توسيعي , V- حلقه , مدول توسيعي , حلقه آرتيني , حلقه نوتري
تاريخ نمايه سازي :
5/3/94
استاد داور :
منصور معتمدي،علي رضا نصر اصفهاني،محمد رضا ودادي
كد ايرانداك :
ID757 دكتري
چكيده انگليسي :
Almost Injective Modules Marzieh Arabi Kakavand m arabikakavand@math iut ac ir February 17 2015 Doctor of Philosophy Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Hossein Khabazian khabaz@cc iut ac ir Advisor Dr Shadi Asgari sh asgari@ipm ir Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran School of Mathematics Institute for Research in Fundamental Sciences IPM Tehran 19395 5746 Iran Abstract In this Thesis the properties of almost injective modules is investigated We provide a negative answer to a question raised by Jain and Alahmadi asking for a possible Baer like criterion for almost injective modules It is shown that there exists an R module M which is almost injective relative to R but not almost injective Also we study the rings R for which every R module is almost injective For such a ring R it is shown that R Soc RR is semisimple and Rad R is fnitely generated It is proved that these rings are exactly Artinian serial rings with Rad R 2 0 if one of these conditions hold Soc RR is fnitely generated RR is extending R is semiperfect or R is of fnite reduced rank Furthermore we introduce the class of right almost V rings A ring R is called a right al most V ring if every simple R module is almost injective It is proved that R is a right almost V ring if and only if for every R module M any complement of every simple submodule of M is a direct summand Moreover R is a right almost V ring if and only if for every simple R module S either S is injective or the injective hull of S is projective of length 2 Right Ar tinian right almost V rings and right Noetherian right almost V rings are characterized A 2 2 upper triangular matrix ring over R is a right almost V ring precisely when R is semisimple Key Words Almost injective modules Right V rings Right almost V rings Artinian se rial rings Essentially injective modules simple extending modules cocyclic modules MSC 2010 16D10 16D70 16D80 Introduction Throughout rings will have unity and modules will be unitary right modules Let M and N be R modules Following 3 M is called almost N injective if for every embedding A N and every homomorphism f A M either there exists a homomorphism g N M such that diagram 1 commutes or there exists a nonzero direct summand D of N with the canonical projection N D and a homomorphism h M D such that diagram 2 commutes 1
استاد راهنما :
حسين خبازيان
استاد داور :
منصور معتمدي،علي رضا نصر اصفهاني،محمد رضا ودادي
