Research Information System
Thesis Type: Postgraduate
Institution Of The Thesis: Marmara University, Institute for Graduate Studies in Pure and Applied Sciences, Department of Mathematics, Turkey
Approval Date: 2011
Thesis Language: Turkish
Student: EMEL ASLANKARAYİĞİT
Supervisor: Ünsal Tekir
Abstract:
The main aim of the study is to describe the concept of the radical classes and the prime radical over the intransitive semirings which were previously defined over the rings and to investigate their features.Firstly, the semiring concept and its basic properties were introduced in the study. Relationships were established between the ideals of the semirings, their homomorphisms; and the ideals of the rings, their homomorphisms. Quotient semirings as the quotient rings? algebraic structure were constructed. Afterwards the main structure of the radical theory on the rings was extended to the semirings. Semisimple classes of semirings, union and intersection of radical classes were examined with the assistance of these expansions. At the end of the study, the Lower Bear Radical for rings was identified in semirings. Then as a result, it was concluded that there was a coincidence between the concept of prime radical defined depending on the radical theory for rings and the Lower Bear Radicals for semirings.