An N-semigroup is a
commutative, cancellative, archimedean semigroup having no idempotents. In the
first section of this paper the Tamura representation of an N-semigroup is used to
determine the translational hull. The maximal semilattice decomposition of the
translational hull is then investigated resulting in a complete determination of the
classes of this decomposition in the case that the N-semigroup is power joined. These
results are used in the second section which deals with ideal extensions of an
N-semigroup by an abelian group, and ideal extensions of an abelian group by an
N-semigroup. These extensions arise naturally in the maximal semilattice
decomposition of a commutative separative semigroup. The latter part of this
section contains results on cancellative extensions of N-semigroups, and a
structure theorem of the class of weakly power joined, commutative, cancellative
semigroups.
