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

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.