پديد آورنده :
رسولي دربكه، محمد
عنوان :
يك رده ي جديد از مونوئيدهاي حاصل ضرب يكتا﴿با كاربرد هايي در نظريه ي حلقه ها﴾
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي محض﴿حلقه و مدول﴾
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
محمدرضا ودادي
توصيفگر ها :
حلقه هاي سري تواني كج , حلقه كاهش , حلقه آرمنداريز
تاريخ نمايه سازي :
8/8/90
استاد داور :
حميد حاج سيد جوادي، محمود بهبودي
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
A new class of unique product monoids Mohammad Rasouli M rasouli derebke iut ac ir June 2011 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr M Reza Vedadi 2000 MSC 51F05 51F20 Key words Artinian narrow unique product monoid Unique product monoid Skew generalized powerseries ring Reduced ring Armendariz ring Abstract In this thesis at rst we remember some de nitions and prerequisite In Section 2 Ar mendariz rings orderly sets unique product group and Artinian narrow sets are discussedextensively A group G is a unique product group a u p group for short if whenever Aand B are nite nonempty subsets of G there is an element of AB that is uniquely expressiblein the form ab with a in A and b in B If A and B are nonempty subsets of a monoid S thenan element s in AB is said to be a unique product element in the product AB of the sets Aand B if it is uniquely presented in the form s ab where a in A and b in B Unique productgroups have been investigated in connection with the Zero Divisor Conjecture which statesthat if R is an associative ring without nonzero zero divisors and G is a torsion free group then the group ring R G contains no nonzero zero divisors Generalizing from groups tomonoids i e to not necessarily commutative semigroups with unity one can de ne uniqueproduct monoids u p monoids for short which have proved instrumental in characterizingsome important classes of monoid rings Let S be an ordered monoid We say that S isan artinian narrow unique product monoid or an a n u p monoid or simply a n u p iffor every two artinian and narrow subsets A and B of S there exists a u p element in theproduct AB Besides expansion of some orderly monoids in Section 3 a new class of them isexpressed A new class of a n u p monoids is propounded as a combination of orderly monoidsand a n u p monoids This new class obtains a proper base for similar results on reduce rings domains and Armendariz rings With some examples logical and important relations amonga n u p monoids will be showed For example it is showed that m a n u p monoids are notquasi totality Totality orderly monoids are not m a n u p monoids intrinsically and a n u pmonoids are not m a n u p monoids necessarily In Section 4 skew generalized power seriesrings are remember that were considered by Marks and Mazurek at 2008 In proceeding ofGroenewald Krempa and park s work we modify skew generalized power series rings andinvestigate an expansion of them in a n u p monoids We use these rings that include largenumber of algebra structures for example skew polynomial rings skew power series ringsand for identi cation of group rings In Proceeding we express conditions that foregoingrings are converted to reduce rings or domain under them Ridig rings are reviewed thenS rigid rings are de nite that S is totality orderly monoid Armendaiz rings were extendedto skew generalized power series rings by Mazurak and Zeimbowski at 2010 At the end alarge number of pre proved results about Armendariz rings are inference using propositionin Section 4 1
استاد راهنما :
محمدرضا ودادي
استاد داور :
حميد حاج سيد جوادي، محمود بهبودي
