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Strongly semiprime rings

1975; Mathematical Sciences Publishers; Volume: 60; Issue: 1 Linguagem: Inglês

10.2140/pjm.1975.60.115

1945-5844

David Handelman,

Rings, Modules, and Algebras

For a ring with 1, we show that every proper kernel functor generates a proper torsion radical if and only if the ring is a finite subdirect product of strongly prime (also called ATF) rings. This is equivalent to every essential right ideal containing a finite set whose right annihilator is zero. We use this characterization to quickly prove a number of properties of rings satisfying this condition, and apply the results to the problem: when is every kernel functor a torsion radical.