Algebraicity of the Radical in Local Rings / I.O. Kachkovskii // Vestn. Mosk. Univ., Matem. Mekhan. 2009. № 6. P. 23-26 [Moscow Univ. Math. Bulletin. Vol. 64, No 6, 2009. P. 249-252.]
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.