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Hypergroup : ウィキペディア英語版
Hyperstructure

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'' = \bigcup_ (a \star 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



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