SYMMETRIC MARTINDALE QUOTIENT RINGS OF ORE EXTENSIONS WITH MORE THAN ONE INDETERMINATE

摘要

Let R be a domain and D a sequence of derivations of R with length >= 2. Let Q(s)((D)) (R) be the subring consisting of those q in the symmetric Martindale quotient ring of R such that qI boolean OR Iq subset of R for a nonzero D-invariant ideal I of R. It is shown here that the symmetric Martindale quotient ring of the Ore extension RX, D is the Ore extension Q(s)((D)) (R)X, D. Our proof depends on an interesting combinatoric result on words.