Geodesic
Algebraicity of the radical in local rings
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2009), pp. 23-26

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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. 
@article{VMUMM_2009_6_a3,
     author = {I. O. Kachkovskii},
     title = {Algebraicity of the radical in local rings},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {23--26},
     publisher = {mathdoc},
     number = {6},
     year = {2009},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2009_6_a3/}
}
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I. O. Kachkovskii. Algebraicity of the radical in local rings. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2009), pp. 23-26. http://geodesic.mathdoc.fr/item/VMUMM_2009_6_a3/