Associative rings

Andrunakievich, V. A.; Arnautov, V. I.; Goyan, I. M.; Ryabukhin, Yu. M.

doi:10.1007/bf01097781

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2011

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Cited by 3 publications

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“…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].…”

Section: Introductionmentioning

confidence: 99%

On Bad Supernilpotent Radicals

France-Jackson¹

2011

Bull. Aust. Math. Soc.

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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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“…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].…”

Section: Introductionmentioning

confidence: 99%