Ore Extensions of Ore Domains

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...

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Bibliographic Details
Published inCommunications in algebra Vol. 43; no. 2; pp. 481 - 502
Main Author Chuang, Chen-Lian
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.02.2015
Subjects
Automorphism
Derivation
Martindale quotient ring
Ore domain
Ore extension
Skew polynomial ring
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Summary: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.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2013.839696