Ore Extensions of Ore Domains

Abstract

Let R be a right Ore domain and φ a derivation or an automorphism of R. We determine the right Martindale quotient ring of the Ore extension R[t; φ] (Theorem 1.1). As an attempt to generalize both the Weyl algebra and the quantum plane, we apply this to rings R such that k[x] ⊆ R ⊆ k(x), where k is a field and x is a commuting variable. The Martindale Quotient quotient ring of R[t; φ] and its automorphisms are computed. In this way, we obtain a family of non-isomorphic infinite dimensional simple domains with all their automorphisms explicitly described.

Key Words:

• Automorphism
• Derivation
• Martindale quotient ring
• Ore domain
• Ore extension
• Skew polynomial ring

2010 Mathematics Subject Classification:

• 16D30
• 16S36
• 16S85
• 16W20
• 16W20
• 16W25

ACKNOWLEDGEMENT

The author thanks the referee for suggesting the consideration of isomorphisms instead of automorphisms in §3, which is more general, natural, and interesting.

Notes

Communicated by E. Kirkman.