The set of minimal distances of the monoid of plus-minus weighted zero-sum sequences and applications to the characterization problem

Abstract

Recently a systematic investigation of monoids of sequences of plus-minus weighted zero-sum sequences had been started, which is among others motivated by applications to monoids of norms of algebraic integers. In the current paper these investigations are continued. The focus is on the set of minimal distances of these monoids, which is an important arithmetical invariant. Applications to the characterization problem are discussed as well.