Hypermathematics, H_v-Structures, Hypernumbers, Hypermatrices and Lie-Santilli Addmissibility

摘要

We present the largest class of hyperstructures called H_v-structures. In H_v-groups and H_v-rings, the fundamental relations are defined and they connect the algebraic hyperstructure theory with the classical one. Using the fundamental relations, the H_v-fields are defined and their elements are called hypernumbers or H_v-numbers. H_v-matrices are defined to be matrices with entries from an H_v-field. We present the related theory and results on hypermatrices and on the Lie-Santilli admissibility.