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The rank of a commutative semigroup

Antonio M. Cegarra, Mario Petrich (2009)

Mathematica Bohemica

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

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