Semilattice decompositions were introduced in the 1950’s and provide the earliest structural insight into commutative semigroups in general, showing, for instance, that finite commutative semigroups are assembled from groups and nilsemigroups arranged along a semilattice. They have been the mainstay of commutative semigroup theory for many years (see e.g. Petrich ).
KeywordsAbelian Group Commutative Semigroup Subdirect Product Positive Power Semi Group
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