Walk Through Weak Hyperstructures, A: Hv-Structures

Contents
Preface
1. Fundamentals of algebraic structures
	1.1 Semigroups and groups
	1.2 Rings
	1.3 Modules
	1.4 Vector space
2. Algebraic hyperstructures
	2.1 Semihypergroup
	2.2 Hypergroups
	2.3 Hyperrings
	2.4 Hypermodules
3. Hv-groups
	3.1 Hv-groups and some examples
	3.2 Enumeration of Hv-groups
	3.3 Fundamental relation on Hv-groups
	3.4 Reversible Hv-groups
	3.5 A sequence of finite Hv-groups
	3.6 Fuzzy Hv-groups
	3.7 Hv-semigroups and noise problem
4. Hv-rings
	4.1 Hv-rings and some examples
	4.2 Fundamental relations on Hv-rings
	4.3 Uniting elements
	4.4 Multiplicative Hv-rings
	4.5 Hv-fields
	4.6 Hv-rings endowed with P-hyperoperations
	4.7 ∂-hyperoperations and Hv-rings
	4.8 (H, R)-Hv-rings
	4.9 The Hv-ring of fractions
	4.10 Hv-group rings
	4.11 Hv-near rings
	4.12 Fuzzy Hv-ideals
5. Hv-modules
	5.1 Hv-modules and fundamental relations
	5.2 Hv-module of fractions
	5.3 Direct system and direct limit of Hv-modules
	5.4 M[-] and -[M] Functors
	5.5 Five short lemma and snake lemma in Hv-modules
	5.6 Shanuel\'s lemma in Hv-modules
	5.7 Product and direct sum in Hv-modules
	5.8 Fuzzy and intuitionistic fuzzy Hv-submodules
6. Hyperalgebra and Lie-Santilli theory
	6.1 Hv-vector space
	6.2 e-hyperstructures
	6.3 The Lie-Santilli\'s admissibility
	6.4 Hv-matrix representations
7. Outline of applications and modeling
	7.1 Chemical examples
		7.1.1 Chain reactions
		7.1.2 Dismutation reactions
		7.1.3 Redox reactions
		7.1.4 Galvanic cell
		7.1.5 Electrolytic cell
		7.1.6 Galvanic/Electrolytic cells
	7.2 Biological examples
		7.2.1 Inheritance examples
		7.2.2 Examples of different types of non-Mendelian inheritance
		7.2.3 Hyperstructures in second generation genotype
		7.2.4 The hypothetical cross of n different traits, case of simple dominance
		7.2.5 The hypothetical cross of n different traits, case of incomplete dominance
		7.2.6 The hypothetical cross of m + n different traits, case of simple and incomplete dominance combined together
	7.3 Physical examples
		7.3.1 Leptons
		7.3.2 The algebraic hyperstructure of Leptons
Bibliography
Index