Non-absolutely irreducible elements in the ring of Integer-valued polynomials

Research output: Contribution to journalArticle

Abstract

Let R be a commutative ring with identity. An element (Formula presented.) is said to be absolutely irreducible in R if for all natural numbers n > 1, r n has essentially only one factorization namely (Formula presented.) If (Formula presented.) is irreducible in R but for some n > 1, r n has other factorizations distinct from (Formula presented.) then r is called non-absolutely irreducible. In this paper, we construct non-absolutely irreducible elements in the ring (Formula presented.) of integer-valued polynomials. We also give generalizations of these constructions.

Original languageEnglish
Pages (from-to)1789-1802
Number of pages14
JournalCommunications in Algebra
Volume48
Issue number4
Early online date4 Jan 2020
DOIs
Publication statusPublished - 2 Apr 2020

Keywords

  • absolutely irreducible elements
  • integer-valued polynomials
  • Irreducible elements
  • non-absolutely irreducible elements

ASJC Scopus subject areas

  • Algebra and Number Theory

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