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Rees matrix semigroups are a special class of semigroup introduced by David Rees in 1940. They are of fundamental importance in semigroup theory because they are used to classify certain classes of simple semigroups. == Definition == Let ''S'' be a semigroup, ''I'' and ''Λ'' non-empty sets and ''P'' a matrix indexed by ''I'' and ''Λ'' with entries ''p''''i'',''λ'' taken from ''S''. Then the Rees matrix semigroup ''M(S;I,Λ;P)'' is the set ''I''×''S''×''Λ'' together with the multiplication :''(i,s,λ)(j,t,μ) = (i, spλ,jt, μ). Rees matrix semigroups are an important technique for building new semigroups out of old ones. 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「Rees matrix semigroup」の詳細全文を読む スポンサード リンク
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