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 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 . Our proof depends on an interesting combinatoric result on words.

Key Words:

• Derivation
• Ore extension
• Skew polynomial ring
• Symmetric Martindale quotient ring

2010 Mathematics Subject Classification:

• 16S70
• 16S36
• 16S85
• 16W25

Notes

Communicated by A. Smoktunowicz.