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Hyperstructure

From Wikipedia, the free encyclopedia

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 nonempty set 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

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  • AHA (Algebraic Hyperstructures & Applications). A scientific group at Democritus University of Thrace, School of Education, Greece. aha.eled.duth.gr
  • Applications of Hyperstructure Theory, Piergiulio Corsini, Violeta Leoreanu, Springer, 2003, ISBN 1-4020-1222-5, ISBN 978-1-4020-1222-8
  • Functional Equations on Hypergroups, László, Székelyhidi, World Scientific Publishing, 2012, ISBN 978-981-4407-00-7