Algebraic structure equipped with at least one multivalued operation
This article is about a mathematical concept. For the architectural concept, see
arcology.
Hyperstructures are
algebraic structures equipped with at least one
multi-valued operation, called a hyperoperation. The largest classes of the hyperstructures are the ones called – structures.
A hyperoperation on a
nonemptyset is a mapping from to the nonempty
power set, meaning the set of all nonempty subsets of , i.e.
For we define
and
is a semihypergroup if is an
associative hyperoperation, i.e. for all
Furthermore, a hypergroup is a semihypergroup , where the
reproduction axiom is valid, i.e.
for all
References
AHA (Algebraic Hyperstructures & Applications). A scientific group at Democritus University of Thrace, School of Education, Greece.
aha.eled.duth.gr