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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.
- 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]
- Subjects :
- *SET theory
*FACTORIZATION
*INTEGERS
*POLYNOMIALS
*DEDEKIND sums
*MAXIMAL ideals
Subjects
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