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- W1601867425 abstract "Let R be a ring with an endomorphism α and an α-derivation δ. In this article, we first compute the Jacobson radical of NI ℤ-graded rings and show that J(S) = Niℓ(S) if and only if is a ℤ-graded NI ring and J(S) ∩ S 0 is nil. As a corollary we show that, J(R[x; α]) = Niℓ(R[x; α]) if and only if R[x; α] is NI and J(R[x; α]) ∩ R ⊆ Niℓ(R). If R[x, x −1; α] is NI we prove that, J(R[x, x −1; α]) = Niℓ(R[x, x −1; α]) = Niℓ*(R[x, x −1; α]) = Niℓ(R)[x, x −1; α]. We also provide necessary and sufficient conditions for a skew polynomial ring R[x; α, δ] and skew Laurent polynomial ring R[x, x −1; α] to be NI." @default.
- W1601867425 created "2016-06-24" @default.
- W1601867425 creator A5028215517 @default.
- W1601867425 date "2015-08-24" @default.
- W1601867425 modified "2023-10-16" @default.
- W1601867425 title "On NI Skew Polynomial Rings" @default.
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- W1601867425 doi "https://doi.org/10.1080/00927872.2014.957385" @default.
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