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Full Screen- Title
- Declaration
- Certificate
- Acknowledgement
- Contents
- Introduction
- 1. Preliminaries
- 1.2 Fuzzy algebra structure
- 1.3 Operation of fuzzy sets
- 1.4 Prime fuzzy ideals, Maximal fuzzy ideals, radicals
- 2. Fuzzy ideals and valuation rings
- 2.2 Level fuzzy ideals
- 2.3 Level fuzzy ideals and valuation rings
- 2.4 Valuation fuzzy ideals
- 2.5 Relationship between level fuzzy ideals and valuation fuzzy ideals
- 3. Fuzzy ideals and Real valuation rings
- 3.3 Value group from R-valuation fuzzy ideals
- 3.4 R-valuation fuzzy ideals in a discrete valuation ring
- 4. P- Fuzzy ideals
- 4.2 Local fuzzy ideals
- 4.4 P- Fuzzy ideals of Dedekind domains
- 4.5 Radical of P- Fuzzy ideals
- 4.6 Fuzzy ideals of Rp and P- Fuzzy ideals
- 4.7 P- Fuzzy ideals of a principal ideal domain
- 5. Fuzzy modules
- 5.2 R- multiples of a fuzzy module
- 5.3 Valuation rings and modules of their quotient fields
- 5.4 R- multiples of fractionary fuzzy ideals
- 5.5 P- Fuzzy modules
- 5.6 Cyclic P- fuzzy modules over Dedekind domains
- 5.7 P- fuzzy modules of free R- modules
- Conclusion
- List of Symbols
- Bibliography