Vol. 60, No. 1, 1975

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Strongly semiprime rings

David E. Handelman

Vol. 60 (1975), No. 1, 115–122

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.

Mathematical Subject Classification
Primary: 16A12
Received: 17 May 1974
Published: 1 September 1975
David E. Handelman