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Bulletin of the London Mathematical Society Advance Access published online on May 7, 2008
Bulletin of the London Mathematical Society, doi:10.1112/blms/bdn040
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© 2008 London Mathematical Society

On minimal distances in Krull monoids with infinite class group

S. T. Chapman

Department of Mathematics
Trinity University
One Trinity Place
San Antonio, TX 78212-7200
USA

W. A. Schmid

Institut für Mathematik und Wissenschaftliches Rechnen
Karl-Franzens-Univer-sität Graz
Heinrichstraße 36
8010 Graz
Austria
wolfgang.schmid@uni-graz.at

W. W. Smith

Department of Mathematics
The University of North Carolina at Chapel Hill
Phillips Hall
Chapel Hill, NC 27599
USA
wwsmith@email.unc.edu

Received 12 June 2007. Revision received 15 January 2008.

Let H be a Krull monoid with infinite class group such that each divisor class contains a prime divisor. It is shown that for every positive integer n, there exists a divisor closed submonoid S of H such that min {Delta}(S)=n.

2000 Mathematics Subject Classification 20K01, 13F05, 11R27.

The second author is supported by the FWF (Project no. P18779 [GenBank] -N13).


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