English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The investigation of the arithmetic of monoids of zero-sum sequences over finite abelian groups is a classical subject due to their crucial role in understanding the arithmetic of (transfer) Krull monoids. More recently, sequences that admit, for a given set of weights, a weighted zero-sum received increased attention. Yet, the focus was on zero-sum constants rather than the arithmetic of the monoids formed by these sequences. We begin a systematic study of the arithmetic of these monoids. We show that for a wide class of weights unions of sets of lengths are intervals and we obtain various results on the elasticity of these monoids. More detailed results are obtained for the special case of plus-minus weighted sequences. Moreover, we apply our results to obtain results on factorizations of norms of algebraic integers.

communications in algebra

Monoids of sequences over finite abelian groups defined via zero-sums with respect to a given set of weights and applications to factorizations of norms of algebraic integers