Research Information System
Thesis Type: Postgraduate
Institution Of The Thesis: Inonu University, Fen-Edebiyat Fakültesi, Matematik, Turkey
Approval Date: 2024
Thesis Language: Turkish
Student: MEHMET EMİN PEKOK
Supervisor: Abdullah Fatih Özcan
Open Archive Collection: AVESIS Open Access Collection
Abstract:
Basic algebraic structures and hyperstructures are discussed together. Algebraic hyperstructures are generalizations of basic algebraic structures. In basic algebraic structure, the operation of two elements is still an element on a defined operation, while in algebraic hyperstructures, the operation of two elements is a non-empty set on a defined operation. The concepts of group, ring, field and module are discussed in basic algebraic structures. Hypergroup, hyperring, hyperfield and hypermodule titles are explained in hyperstructures. In the first chapter, an introduction to the subject has been made. In the second part, basic algebraic structures are given. In the third chapter, the concept of hypergroup is explained with examples and subheadings. In the fourth chapter, hyperring concepts are introduced and Krasner hyperring and multiplicative hyperrings are explained with examples. In the fifth chapter, hyperfield and hypermodule titles are included.