The constant part of the Jacobson radical of R[x;σ,δ] is nil, and in char 0 the full radical equals N[x;σ,δ] for some nil ideal N of R.
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On a $q$-Skew Amitsur's Theorem
The constant part of the Jacobson radical of R[x;σ,δ] is nil, and in char 0 the full radical equals N[x;σ,δ] for some nil ideal N of R.