Vol. 41, No. 2, 1972

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The translational hull of an N-semigroup

Robert E. Hall

Vol. 41 (1972), No. 2, 379–389

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.

Mathematical Subject Classification 2000
Primary: 20M10
Received: 25 February 1971
Revised: 11 February 1972
Published: 1 May 1972
Robert E. Hall