پديد آورنده :
مولايي ساماني، زيبا
عنوان :
راديكال پوچ بالايي كوته براي مدول ها
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
استاد راهنما :
محمود بهبودي
استاد مشاور :
عاطفه قرباني
واژه نامه :
به فارسي و انگليسي
توصيفگر ها :
زير مدول s-اول , كلاس ويژه مدول ها و s- سيستم مدول ها
تاريخ نمايه سازي :
1394/09/15
استاد داور :
محمدرضا ودادي، عليرضا نصراصفهاني
تاريخ ورود اطلاعات :
1396/10/05
چكيده انگليسي :
Kothe s Upper Nil Radical For Modules Ziba Molaei Samani Z molayisamani@math iut ac ir Aug 8 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mahmood Behboodi mbehbood@cc iut ac ir Advisor Dr Atefeh Ghorbani a ghorbani@cc iut ac ir 2010 MSC 16D60 16N40 16N60 16N80 16S90 Keywords s prime module upper nil radical Kothe s upper nil radical s system of modules Abstract This thesis is based on the works on the paper Kothe s upper nil radical for modules by N J Groenewald and D Ssevviiri in Acta Math Hungar 138 4 2013 295 306 Let M be a left R module A proper submodule P of M is called prime if for each ideal A of R andeach submodule N of M if AN P then AM P or N P A proper submodule P of M is calleda classical prime submodule if for all ideals A B of R and for each submodule N of M if ABN P then AN P or BN P and also a proper submodule P of M is called s prime if for each ideal Aof R and for each submodule N of M and for any elements x A if there exsites a nonzero positiveinteger n such that xn N P then N P or AM P In this paper generalizations of this notionsof s system and m system of rings to modules are given It is clear that for a two sided ideal I of any ring R I is an s prime resp prime ideal if andonly if it is an s prime resp prime submodule of M R Therefore in case M R where R is acommutative ring s prime resp prime submodules coincides whit s prime resp prime ideals In ring theory prime ideals are closely to m system sets A nonempty set S R is called m systemif for each a b S then exsites r R such that arb S For an ideal P of R P is a prime ideal if andonly if S R P is an m system Let M be an R mobule A nonempty set S M 0 is said to be ans system set if for each A R and for K L M if K L S and K AM S Then thereexists x A such that K xn L S for every n N The complement of an s prime moduleis an s system and given an s system set S a module disjoint from S and maximal with respect tothis property is always an s prime module It is easy to see that every s system set is an m system
استاد راهنما :
محمود بهبودي
استاد مشاور :
عاطفه قرباني
استاد داور :
محمدرضا ودادي، عليرضا نصراصفهاني
