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

JOURNAL OF ALGEBRA

卷:528

Article

Frisch, Sophie¹  Nakato, Sarah²  Rissner, Roswitha² 

[1] Graz Univ Technol, Inst Anal & Zahlentheorie, Kopernikusgasse 24, A-8010 Graz, Austria

[2] Alpen Adria Univ Klagenfurt, Inst Math, Univ Str 65-67, A-9020 Klagenfurt Am Worthersee, Austria

关键词: Factorizations;    Sets of lengths;    Integer-valued polynomials;    Dedekind domains;    Block monoid;    Transfer homomorphism;    Krull monoid;    Monadically Krull monoid;   

DOI  :  10.1016/j.jalgebra.2019.02.040

来源: Elsevier

【 摘 要 】

Let D be a Dedekind domain with infinitely many maximal ideals, all of finite index, and K its quotient field. Let Int (D) = { f is an element of K[x] vertical bar f(D) subset of 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. (C) 2019 The Authors. Published by Elsevier Inc.

【 授权许可】

Free