Functional degrees and arithmetic applications I: The set of functional degrees

Uwe Schauz*, Pete L. Clark

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We give a further development of the Aichinger-Moosbauer calculus of functional degrees of maps between commutative groups. For any finitely generated commutative groups A and B, we compute the complete set D(A,B) of functional degrees of all maps between A and B. In particular, we see how big the functional degree of a function with finite functional degree can get, in which cases there is a maximal finite functional degree, and when there are functions of infinite functional degree between A and B. This yields a solution to Aichinger and Moosbauer's problem of finding the nilpotency index of the augmentation ideal of group rings of the form Zpβ[Zpα1×Zpα2×⋯×Zpαn] with p,β,n,α1,…,αn∈Z+, p prime.

Original languageEnglish
Pages (from-to)691-718
Number of pages28
JournalJournal of Algebra
Publication statusPublished - 15 Oct 2022


  • Abelian groups
  • Functional degree
  • Polynomial functions


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