科研之友
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摘要
A special atom (respectively, supernilpotent atom) is a minimal element of the lattice S of all special radicals (respectively, a minimal element of the lattice K of all supernilpotent radicals). A semiprime ring R is called prime essential if every nonzero prime ideal of R has a nonzero intersection with each nonzero two-sided ideal of R. We construct a prime essential ring R such that the smallest supernilpotent radical containing R is not a supernilpotent atom but where the smallest special radical containing R is a special atom. This answers a question put by Puczylowski and Roszkowska.
- 出版日期2017-4
