Back to Search
Start Over
A note on integer-valued skew polynomials.
- Source :
- Journal of Algebra & Its Applications; Aug2023, Vol. 22 Issue 8, p1-13, 13p
- Publication Year :
- 2023
-
Abstract
- Given an integral domain D with quotient field K , the study of the ring of integer-valued polynomials Int (D) = { f ∈ K [ X ] | f (a) ∈ D for all a ∈ D } has attracted a lot of attention over the past decades. Recently, Werner has extended this study to the situation of skew polynomials. To be more precise, if σ is an automorphism of K , one may consider the set Int (D , σ) = { f ∈ K [ X , σ ] | f (a) ∈ D for all a ∈ D } , where K [ X , σ ] is the skew polynomial ring and f (a) is a "suitable" evaluation of f at a. For example, he gave sufficient conditions for Int (D , σ) to be a ring and study some of its properties. In this paper, we extend the study to the situation of the skew polynomial ring K [ X , σ , δ ] with a suitable evaluation, where δ is a σ -derivation. Moreover we prove, for example, that if σ is of finite order and D is a Dedekind domain with finite residue fields such that Int (D , σ) is a ring, then Int (D , σ) is non-Noetherian. [ABSTRACT FROM AUTHOR]
- Subjects :
- POLYNOMIAL rings
POLYNOMIALS
FINITE fields
NOETHERIAN rings
Subjects
Details
- Language :
- English
- ISSN :
- 02194988
- Volume :
- 22
- Issue :
- 8
- Database :
- Complementary Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 164158514
- Full Text :
- https://doi.org/10.1142/S0219498823501712