Fuzzy ideal of semigroup

This thesis is a review study, and it does not contain any original results. All the definitions, theorems, examples, etc. given in the thesis are very well-known in the literature of this area; thus, some of them are presented without mentioning any source, however for lots of them, a relevant source is cited. Two of the main sources used in the preparation of the thesis are Asaad and Mohammed (2019), and Mohammed and Asaad (2019). The main objective of the thesis is to study, as understood from the title, fuzzy ideal of a semigroup. In the first chapter, named as "introduction", a brief literature review and a summary of the thesis are given. In the second chapter, named as "background and basic concepts", basic and essential definitions and theorems about semigroups and fuzzy subsets of a semigroup are briefly introduced. In the third chapter, fuzzy ideals of a semigroup and a strongly π-regular semigroup are concisely studied. In the fourth chapter, fuzzy ideals of a strongly π-regular ordered semigroup, a π-regular semigroup, and an S-weakly regular semigroup are presented. Finally, the thesis is completed with a concise conclusions and recommendation chapter.