Philosophical suggestions by the single elements

The largest class of hyperstructures is the one which satisfy the weak properties. These are called Hv-structures introduced in 1990 and they proved to have a lot of applications on several applied sciences. Special classes of elements appeared to have new interesting properties applicable in other sciences. We present some results on hyperstructures containing ‘single’ elements, and some new constructions.Keywords: hyperstructures; Hv-structures; single elements

Hyperstructures in Lie-Santilli Admissibility and Iso-Theories

In the quiver of hyperstructures Professor R. M. Santilli, in early 90'es, tried to find algebraic structures in order to express his pioneer Lie-Santilli's Theory. Santilli's theory on 'isotopies' and 'genotopies', born in 1960's, desperately needs 'units e' on left or right, which are nowhere singular, symmetric, real-valued, positive-defined for n-dimensional matrices based on the so called isofields.These elements can be found in hyperstructure theory, especially in $H_v$-structure theory introduced in 1990. This connection appeared first in 1996 and actually several $H_v$-fields, the e-hyperfields, can be used as isofields or genofields so as, in such way they should cover additional properties and satisfy more restrictions. Several large classes of hyperstructures as the P-hyperfields, can be used in Lie-Santilli's theory when multivalued problems appeared, either in finite or in infinite case. We review some of these topics and we present the Lie-Santilli admissibility in Hyperstructures