Abstract:
In this paper we continue the study of algebraic subsets of noncommutative local rings. (A subset of a ring is said to be algebraic if there exists a monic polynomial with coefficients from the ring vanishing on the subset.) In particular, we prove that the Jacobson radical of a local ring is an algebraic subset if and only if it is a nil ideal of a bounded index.
Key words:skew polynomials, noncommutative local ring, roots of polynomials, algebraicity of subsets, Jacobson radical.
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