Abstract
An irreducible element of a commutative ring is absolutely irreducible if no power of it has more than one (essentially different) factorization into irreducibles. In the case of the ring (Formula presented.) of integer-valued polynomials on a principal ideal domain D with quotient field K, we give an easy to verify graph-theoretic sufficient condition for an element to be absolutely irreducible and show a partial converse: the condition is necessary and sufficient for polynomials with square-free denominator.
| Original language | English |
|---|---|
| Pages (from-to) | 3716-3723 |
| Number of pages | 8 |
| Journal | Communications in Algebra |
| Volume | 48 |
| Issue number | 9 |
| Early online date | 3 Apr 2020 |
| DOIs | |
| Publication status | Published - 1 Sept 2020 |
Keywords
- factorization
- non-unique factorization
- irreducible elements
- absolutely irreducible elements
- atoms
- strong atoms
- atomic domains
- integer-valued polynomials
- simple graphs
- connected graphs
- Factorization
ASJC Scopus subject areas
- Algebra and Number Theory
Fields of Expertise
- Information, Communication & Computing