This chapter contains a global construction of subcomplete semigroups, as quotients of free commutative monoids; complete semigroups, finite semigroups, subelementary semigroups, and finitely generated semigroups are particular cases. In particular, this constructs all congruences on finitely generated free commutative monoids. The construction uses Ponizovsky families to generalize the results in Chapter X and relates smoothly to related structural features including archimedean components, subdirect decompositions, К-classes, and extended Schützenberger functors. Its relationship to extension groups is less obvious and is shown in Section XIII.2. A similar construction was obtained by the author for finite congruences [1996C], then generalized to complete group-free congruences [2001C].
KeywordsSemilattice Congruence Cancellative Monoid Archimedean Component Direction Face Extent Cell
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