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The 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 ''Hv'' – structures. A hyperoperation ( *) on a non-empty set ''H'' is a mapping from ''H'' × ''H'' to power set ''P'' *(''H'') (the set of all non-empty sets of ''H''), i.e. ( *): ''H'' × ''H'' → ''P'' *(''H''): (''x'', ''y'') → ''x'' *''y'' ⊆ ''H''. If ''Α'', ''Β'' ⊆ ''Η'' then we define : ''A'' *''B'' = and ''A'' *''x'' = ''A'' *, ''x'' *''B'' = * ''B''. (''Η'', *) is a ''semihypergroup'' if ( *) is an associative hyperoperation, i.e. ''x'' *(''y'' *''z'') = (''x'' *''y'') *''z'', for all ''x'',''y'',''z'' of ''H''. Furthermore, a ''hypergroup'' is a semihypergroup (''H'', *), where the reproduction axiom is valid, i.e. ''a'' *''H'' = ''H'' *''a'' = ''H'', for all ''a'' of ''H''. ==References== *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 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hyperstructure」の詳細全文を読む スポンサード リンク
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