On the semisimplicity of skew polynomial rings
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- by Jai Ram PDF
- Proc. Amer. Math. Soc. 90 (1984), 347-351 Request permission
Abstract:
Let $R$ be a ring satisfying the maximal condition on annihilator left ideals and $\sigma$ be an automorphism of $R$. We show that the Jacobson radical of the skew polynomial ring ${R_\sigma }[x]$ is nonzero if and only if the prime radical of ${R_\sigma }[x]$ is nonzero. Furthermore, it is so if and only if the prime radical of $R$ is nonzero. In general, an example is given of a commutative semisimple algebra $R$ and an automorphism $\sigma$ such that ${R_\sigma }[x]$ is prime but the Levitzki radical of ${R_\sigma }[x]$ is nonzero.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 90 (1984), 347-351
- MSC: Primary 16A05; Secondary 16A12, 16A20
- DOI: https://doi.org/10.1090/S0002-9939-1984-0728345-7
- MathSciNet review: 728345