The local semilattice of chains of idempotents.
The concept of rank of a commutative cancellative semigroup is extended to all commutative semigroups by defining as the supremum of cardinalities of finite independent subsets of . Representing such a semigroup as a semilattice of (archimedean) components , we prove that is the supremum of ranks of various . Representing a commutative separative semigroup as a semilattice of its (cancellative) archimedean components, the main result of the paper provides several characterizations...