8277

7675

كارشناسي ارشد

رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده رياضي

1392

نه، 73ص

ص.ع:به فارسي و انگليسي

محمد رضا ودادي

حسين خبازيان

25/09/1392

محمود بهبودي، عاطفه قرباني

رياضي

ID7675

به فارسي و انگليسي: قابل رويت در نسخه ديجيتال

Weak Annihilator over Extension Rings Neda Zamani Gandomani nedazamani@math iut ac ir 2013 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr MohammadReza Vedadi mrvedadi@cc iut ac ir Advisor Dr Hossein Khabazian khabaz@cc iut ac ir 2010 MSC 13B25 16N60 Keywords Weak annihilator nilpotent associated prime nilpotent good polynomial AbstractThis thesis is an extension and generalization of the work s done by Faith 12 For a subset X ofa ring R the right annihilator of X in R is defined by set of a R xa 0 x X and denoted byrR X The left annihilator of X in R is defined similarly and denoted by lR X As a generalizationof the right left annihilator we introduce the notion of a weak annihilator of a subset in a ring Weakannihilator of X in R is defined by set of a R xa nil R x X which denoted by NR X IfX is singleton say X x we use NR x in place of NR X We introduce Ore extension ring anddenoted by R x whose elements s are the polynomials over R The addition is defined as usualand the multiplication subject to the relation ab a b a b for any a R In this thesis weinvestigate the weak annihilator properties over the Ore extension ring We prove that set of nipotentelements of ring R is an ideal in R if and only if for each subset X of R weak annihilator of X inR is an ideal in R Assume that X and Y be subsets in R We prove that if X be subset of Y weakannihilator of X in R contains weak annihilator of Y in R We show that weak annihilator of weakannihilator of X in R contains X and weak annihilator of weak annihilator of weak annihilator of X inR is equall weak annihilator of X in R Let be an derivation of R For integers i j with 0 i j fij End R will denote the map which is the sum of all possible words in built with i letters and j i letters Let R be an compatible Then we show that if for every a b c R abc 0then for every 0 i j abfij c 0 and afij b c 0 We prove that if for each a b R ab nil R then for each j i 0 afij b nil R Too we show that if for each a b R and a positive integerm a m b nil R then ab nil R Let R be an compatible and P R nil R Then we showthat every nilpotent element of R x is exactly a element of R x that it s coefficients are inR are nilpotent and Then we result that set of nilpotent elements R x is an ideal in R x If

محمد رضا ودادي

حسين خبازيان

محمود بهبودي، عاطفه قرباني