Symmetric Martindale Quotient Rings of Ore Extensions with More than One Indeterminate

Abstract

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