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

Abstract

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