Quasi-half-factorial subsets of abelian torsion groups

• Autores: Scott T. Chapman, W. A. Schmid, William W. Smith
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 35, Nº 1, 2009, págs. 13-22
• Idioma: inglés
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• Resumen

  • If G is an abelian torsion group with generating subset G0, then by a classical result in the theory of non-unique factorizations, the block monoid B(G0) is a half-factorial monoid if each of its atoms has cross number 1. In this case, G0 is called a half-factorial set. In this note, we introduce the notion of a k-quasi-half-factorial set and show for many abelian torsion groups that G0 k-quasi-half-factorial implies that G0 is half-factorial. We moreover show in general that G0 k-quasi-half-factorial implies that G0 is weakly half factorial, a condition which has been of interest in the recent literature.