Abstract
Let $D$ be a Dedekind domain with infinitely many maximal ideals,
all of finite index, and $K$ its quotient field. Let
$\Int(D) = \{f\in K[x] \mid f(D) \subseteq D\}$ be the ring of
integer-valued polynomials on $D$.
Given any finite multiset $\{k_1, \ldots, k_n\}$ 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 $k_1$, \ldots,
$k_n$. We also show that there is no transfer homomorphism from the
multiplicative monoid of $\Int(D)$ to a block monoid.
all of finite index, and $K$ its quotient field. Let
$\Int(D) = \{f\in K[x] \mid f(D) \subseteq D\}$ be the ring of
integer-valued polynomials on $D$.
Given any finite multiset $\{k_1, \ldots, k_n\}$ 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 $k_1$, \ldots,
$k_n$. We also show that there is no transfer homomorphism from the
multiplicative monoid of $\Int(D)$ to a block monoid.
Originalsprache | englisch |
---|---|
Seiten (von - bis) | 231-249 |
Seitenumfang | 13 |
Fachzeitschrift | Journal of Algebra |
Jahrgang | 528 |
DOIs | |
Publikationsstatus | Veröffentlicht - Juni 2019 |
Fields of Expertise
- Information, Communication & Computing