On bad supernilpotent radicals

Authors

  • Halina France-Jackson

Keywords:

supernilpotent radical, special radical, prime radical, Boolean rings, prime essential rings

Abstract

A supernilpotent radical alpha is called bad if the class of all prime and alpha-semisimple rings consists of the one-element ring 0 only. We construct infinitely many bad supernilpotent radicals which forms a generalization of Rjabukhin'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. DOI: 10.1017/S0004972711003066

Published

2012-02-27

Issue

Vol. 85 No. 2 (2012)

Section

Articles
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