Hyperstructures and Their Representations

algebra associated b₂ canonical hypergroup commutative cyclic group defined as follows DEFINITION Let distributivity is valid equivalence relation f₂ finite sets fundamental class fundamental group fundamental relation fundamental ring groupoid H H H H-field H-group H H-matrix representation H-semigroup H-structure H₁ h₂ homomorphism hypergroupoid hypermatrices hyperoperation hyperproduct hyperstructures hypersum identities of f incidence matrix inclusion distributivity induced representation inner generalized permutation inverse inverse elements isomorphism Let G Let H let us suppose M₂ matrix minimal Moreover multiplicative H-ring obtained obviously P-hyperoperations P>+a P₁ polygroups prove quotient quotient set Remark reproduction axiom resp respect S-construction s₁ scalar scalar partial semigroup set H sets of indices Similarly single elements singleton smallest equivalence relation subhypergroup subset THEOREM Let thin hypergroup thin hyperring transitive closure unit element v₁ WASS zero ΕΙ уєн хен