Algebraicity of the radical in local rings / I. O. Kachkovskii. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2009. № 6. P. 23-26 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. 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.