توصيفگر ها :
مورفيك نما , مورفيك , شبه مورفيك , شبه فروبنيوس , حلقه هاي خاص و ايده آل اصلي آرتيني , تزريقي اصلي راست , مينيمم - تزريقي , متناهي - كش
چكيده انگليسي :
Pseudo Morphic Rings Zohreh Hashempoor z hashempoor@math iut ac ir 2017 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Atefeh Ghorbani a ghorbani@cc iut ac ir Advisor Dr Mohammadreza Vedadi mvedadi@cc iut ac ir 2010 MSC 16L60 16D50 16P60 16U99 Keywords Pseudo Morphic Morphic Quasi Morphic Quasi Frobenius Abstract This M Sc thesis is based on the following paperV Camillo and W K Nicholson On Rings Where Left Principal Ideals Are Left PrincipalAnnihilators called left pseudo morphic by Yang International Electronic Journal of Algebra Vol ume 17 2015 199 214Throughout this review of thesis every ring R is associative with unity and all modules are unitary We write the Jacobson radical as J J R The ring of n n matrices over R will be denoted byMn R and we denote the ring of integers by Z and write Zn for the ring of integers modulo n Call aleft ideal L a left principal annihilator if L l a r R ra 0 for some a R Call an elementa R a left pseudo morphic element if Ra l b for some b R equivalently R Ra embeds in R R Hence a ring R is left pseudo morphic if every element has this property We use similar de nitions onthe right and a ring that is right and left pseudo morphic is called simply pseudo morphic ring Everyregular element is left and right pseudo morphic so regular rings are pseudo morphic However aswe shall see Zn is pseudo morphic for every n 2 For another example every classical artinianprincipal ideal ring is pseudo morphic A ring R is called left quasi morphic if for every a R wehave Ra l b and l a Rc for some b c R If b c for each a R is called left morphic Theserings are clearly left pseudo morphic A ring R is called left special if R is left morphic local and J isnilpotent These rings are all left pseudo morphic It is proved that no upper triangular matrix ringis left or right pseudo morphic A ring R is called reversible if ab 0 implies ba 0 We show that if R is a reversible ring then left pseudo morphic left morphic and left quasi morphic are equivalent
