%0 Journal Article
%T On the delta set and the Betti elements of a BF-monoid
%A S. T. Chapman
%A P. A. Garc¨ªa-S¨¢nchez
%A D. Llena
%A A. Malyshev
%A D. Steinberg
%J Arabian Journal of Mathematics
%@ 2193-5351
%D 2012
%I 
%R 10.1007/s40065-012-0019-0
%X We examine the Delta set of a cancellative and reduced atomic monoid S where every set of lengths of the factorizations of each element in S is bounded. In particular, we show the connection between the elements of ¦¤(S) and the Betti elements of S. We prove how the minimum and maximum element of ¦¤(S) can be determined using the Betti elements of S. This leads to a determination of when ¦¤(S) is a singleton. We then apply these results to the particular case where S is a numerical monoid that requires three generators. Conclusions are drawn in the cases where S has a unique minimal presentation, or has multiplicity three.
%K 20M14
%K 11D07
%K 05C70
%U http://link.springer.com/article/10.1007/s40065-012-0019-0