TY - JOUR
T1 - Polynomials with a common composite
AU - Beals, Robert M.
AU - Wetherell, Joseph L.
AU - Zieve, Michael E.
PY - 2009/11
Y1 - 2009/11
N2 - Let f and g be nonconstant polynomials over a field K. In this paper we study the pairs (f, g) for which the intersection K[f] ∩ K[g] is larger than K. We describe all such pairs in case K has characteristic zero, as a consequence of classical results due to Ritt. For fields K of positive characteristic we present various results, examples, and algorithms.
AB - Let f and g be nonconstant polynomials over a field K. In this paper we study the pairs (f, g) for which the intersection K[f] ∩ K[g] is larger than K. We describe all such pairs in case K has characteristic zero, as a consequence of classical results due to Ritt. For fields K of positive characteristic we present various results, examples, and algorithms.
UR - http://www.scopus.com/inward/record.url?scp=74249094761&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=74249094761&partnerID=8YFLogxK
U2 - 10.1007/s11856-009-0105-y
DO - 10.1007/s11856-009-0105-y
M3 - Article
AN - SCOPUS:74249094761
SN - 0021-2172
VL - 174
SP - 93
EP - 117
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -