Lie-Santilli admissible hyper-structures, from numbers to Hv-numbers

Abstract

The class of Hv-structures defined on a set is very big and admits a partial order. For this reason, it has a numerous of applications in mathematics and other sciences as physics, biology, linguistics, to mention but a few. Here, we focus on the Lie-Santilli’s admissible case, where the hyper-numbers, called Hv-numbers, are used. In order to verify all needed axioms for Lie-Santilli’s admissibility, as the irreversibility and uniqueness of living organisms and time, on the one side and small results on the other side, we use the verythin Hv-fields. Therefore, we take rings and we enlarge only one result by adding only one element in order to obtain an Hv-field. This means that, we use only the associativity on the product and we transfer this to the weak-associativity on the hyper-product. Thus, from a semigroup on the product, we construct an Hv-group on the hyper-product.