TY - JOUR
T1 - Non-absolutely irreducible elements in the ring of Integer-valued polynomials
AU - Nakato, Sarah
PY - 2020/4/2
Y1 - 2020/4/2
N2 - 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.
AB - 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.
KW - absolutely irreducible elements
KW - integer-valued polynomials
KW - Irreducible elements
KW - non-absolutely irreducible elements
UR - http://www.scopus.com/inward/record.url?scp=85077884962&partnerID=8YFLogxK
UR - http://creativecommons.org/licenses/by/4.0/
U2 - 10.1080/00927872.2019.1705474
DO - 10.1080/00927872.2019.1705474
M3 - Article
SN - 0092-7872
VL - 48
SP - 1789
EP - 1802
JO - Communications in Algebra
JF - Communications in Algebra
IS - 4
ER -