Factorization in group algebras

Abstract

Let [Formula: see text] be a field, and let [Formula: see text] be a torsion-free abelian group. In this paper, we study some factorization properties in the group algebra of [Formula: see text] over [Formula: see text], [Formula: see text]. Among other results, we obtain necessary and sufficient conditions in order that [Formula: see text] should be an idf-domain. As an application, we get various results concerning factorization in [Formula: see text].