Abstract:Hypergroups are lifted to power semigroups with negation, yielding a method of transferring results from semigroup theory. This applies to analogous structures such as hypergroups, hyperfields, and hypermodules, and permits us to transfer the general theory espoused in [19] to the hypertheory.Definition 1.1. A monoid (A, •, 1) acts on a set S if there is a multiplication A × S → S satisfying 1s = s and (a 1 a 2 )s = a 1 (a 2 s) for all a i ∈ A and s ∈ S.A pre-semiring (A, •, +, 1) is a multiplicative monoid (A… Show more
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