Let R be a right Ore domain and phi a derivation or an automorphism of R. We determine the right Martindale quotient ring of the Ore extension Rt; phi Theorem 1.1). As an attempt to generalize both the Weyl algebra and the quantum plane, we apply this to rings R such that kx subset of R subset of k(x), where k is a field and x is a commuting variable. The Martindale Quotient quotient ring of Rt; phi 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.
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