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Split absolutely irreducible integer-valued polynomials over discrete valuation domains.
- Source :
-
Journal of Algebra . Jul2022, Vol. 602, p247-277. 31p. - Publication Year :
- 2022
-
Abstract
- Regarding non-unique factorization of integer-valued polynomials over a discrete valuation domain (R , M) with finite residue field, it is known that there exist absolutely irreducible elements, that is, irreducible elements all of whose powers factor uniquely, and non-absolutely irreducible elements. We completely and constructively characterize the absolutely irreducible elements among split integer-valued polynomials. They correspond bijectively to finite sets, which we call balanced , characterized by a combinatorial property regarding the distribution of their elements among residue classes of powers of M. For each such balanced set as the set of roots of a split polynomial, there exists a unique vector of multiplicities and a unique constant so that the corresponding product of monic linear factors times the constant is an absolutely irreducible integer-valued polynomial. This also yields sufficient criteria for integer-valued polynomials over Dedekind domains to be absolutely irreducible. [ABSTRACT FROM AUTHOR]
- Subjects :
- *IRREDUCIBLE polynomials
*FINITE fields
*VALUATION
*POLYNOMIALS
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 602
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 156420439
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2022.03.006