“…Therefore, Andrunakievich [1] asked whether every supernilpotent radical is special. Examples of nonspecial supernilpotent radicals were given in [3,4,6,7,12,14,15].…”
A supernilpotent radical α is called bad if the class π(α) of all prime and α-semisimple rings consists of the one-element ring 0 only. We construct infinitely many bad supernilpotent radicals which form a generalization of Ryabukhin's example of a supernilpotent nonspecial radical. We show that the family of all bad supernilpotent radicals is a sublattice of the lattice of all supernilpotent radicals and give examples of supernilpotent radicals that are not bad.2010 Mathematics subject classification: primary 16N80.
“…Therefore, Andrunakievich [1] asked whether every supernilpotent radical is special. Examples of nonspecial supernilpotent radicals were given in [3,4,6,7,12,14,15].…”
A supernilpotent radical α is called bad if the class π(α) of all prime and α-semisimple rings consists of the one-element ring 0 only. We construct infinitely many bad supernilpotent radicals which form a generalization of Ryabukhin's example of a supernilpotent nonspecial radical. We show that the family of all bad supernilpotent radicals is a sublattice of the lattice of all supernilpotent radicals and give examples of supernilpotent radicals that are not bad.2010 Mathematics subject classification: primary 16N80.
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