Vol. 93, No. 1, 1981

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Closed factors of normal Z-semimodules

Daniel Alan Marcus

Vol. 93 (1981), No. 1, 121–146

Let M be a set of positive integers which is closed under multiplication and division whenever possible: if m,n M and mn, then n∕m M. A closed factor of M is a subset K M which is closed under multiplication and for which there is another subset R M such that every member of M is uniquely representable as a product kr with k K and r R. A theory is developed for determining all closed factors of a given M. The theory can be adapted to an analogous problem for convex polyhedral cones.

Mathematical Subject Classification 2000
Primary: 05A99
Secondary: 20F99, 10A99
Received: 2 August 1979
Published: 1 March 1981
Daniel Alan Marcus