Some Researches On Γ-hemirings

In this thesis, some properties and structures of Γ-hemirings based on the theories of hemirings are studied by means of fuzzy set theory and soft set theory. The whole thesis is composed of four chapters.In the first chapter, we provide a sketch of the historical situation and the present development of relevant subjects about fuzzy algebras, fuzzy soft algebras and hemirings as well as the main work done in this paper. Also, some preliminaries on Γ-hemirings, fuzzy h-ideals and soft sets are given.In the second chapter, we establish the concepts and structures of fuzzy Γ-hemirings with operators, and discuss the Cartesian products of fuzzy Γ-hemirings with operators.In the third chapter, on the basic of fuzzy Γ-hemirings with operators,we define three kinds of fuzzy(h-, h-bi-, h-quasi-)ideals with operators, and depict some particular (h-hemiregular,h-intra-hemiregular,h-quasi-hemiregular) Γ-hemirings with operators by using these fuzzy (h-,h-bi-, h-quasi-) ideals. Finally, we discuss their related characterizations and properties.In the forth chapter, we introduce a new kind of soft Γ-hemirings called soft intersection Γ-hemirings by soft set theory, and furthermore study some related properties and characterizations.