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

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung


Let R be a commutative ring with identity. An element r∈R is said to be absolutely irreducible in R if for all natural numbers n > 1, rn has essentially only one factorization namely rn=r⋯r. If r∈R is irreducible in R but for some n > 1, rn has other factorizations distinct from rn=r⋯r, then r is called non-absolutely irreducible. In this paper, we construct non-absolutely irreducible elements in the ring Int(Z)={f∈Q[x]|f(Z)⊆Z} of integer-valued polynomials. We also give generalizations of these constructions.
FachzeitschriftCommunications in Algebra
Frühes Online-Datum4 Jan 2020
PublikationsstatusElektronische Veröffentlichung vor Drucklegung. - 4 Jan 2020


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