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In mathematics, the Munn semigroup is the inverse semigroup of isomorphisms between principal ideals of a semilattice (commutative semigroup of idempotents). ==Construction's steps== Let be a semilattice. 1) For all ''e'' in ''E'', we define ''Ee'': = which is a principal ideal of ''E''. 2) For all ''e'', ''f'' in ''E'', we define ''T''''e'',''f'' as the set of isomorphisms of ''Ee'' onto ''Ef''. 3) The Munn semigroup of the semilattice ''E'' is defined as: ''T''''E'' := . The semigroup's operation is composition of mappings. In fact, we can observe that ''T''''E'' ⊆ ''I''''E'' where ''I''''E'' is the symmetric inverse semigroup because all isomorphisms are partial one-one maps from subsets of ''E'' onto subsets of ''E''. The idempotents of the Munn semigroup are the identity maps 1''Ee''. 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「Munn semigroup」の詳細全文を読む スポンサード リンク
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