Sets of lengths of factorizations of integer-valued polynomials on Dedekind domains with finite residue fields

@article{Frisch2019SetsOL,
  title={Sets of lengths of factorizations of integer-valued polynomials on Dedekind domains with finite residue fields},
  author={S. Frisch and Sarah Nakato and Roswitha Rissner},
  journal={Journal of Algebra},
  year={2019},
  volume={528},
  pages={231-249}
}
  • S. Frisch, Sarah Nakato, Roswitha Rissner
  • Published 2019
  • Mathematics
  • Journal of Algebra
  • Abstract Let D be a Dedekind domain with infinitely many maximal ideals, all of finite index, and K its quotient field. Let Int ( D ) = { f ∈ K [ x ] | f ( D ) ⊆ D } be the ring of integer-valued polynomials on D. Given any finite multiset { k 1 , … , k n } of integers greater than 1, we construct a polynomial in Int ( D ) which has exactly n essentially different factorizations into irreducibles in Int ( D ) , the lengths of these factorizations being k 1 , …, k n . We also show that there is… CONTINUE READING
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