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Strongly semiprime
rings
David E. Handelman |
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Vol. 60 (1975), No. 1, 115–122
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Abstract |
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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
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Milestones
Received: 17 May 1974
Published: 1 September 1975
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Authors |
| David E. Handelman | |
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