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

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

Authors :
Frisch, Sophie
Nakato, Sarah
Rissner, Roswitha
Source :
Journal of Algebra. Jun2019, Vol. 528, p231-249. 19p.
Publication Year :
2019

Abstract

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 no transfer homomorphism from the multiplicative monoid of Int (D) to a block monoid. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00218693
Volume :
528
Database :
Academic Search Index
Journal :
Journal of Algebra
Publication Type :
Academic Journal
Accession number :
135914739
Full Text :
https://doi.org/10.1016/j.jalgebra.2019.02.040