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Simple Proof of a Theorem and a Result on Γ-Rings

Zhu Yiquan  
This paper gives a simple proof of the well-known theorem (given in[1]) "Let R be a Γ-ring satisfying the ascending chain condition on left divisors of zero. Then every strongly nil one-sided ideal is strongly nilpotent. "Similarly, we can estatablish the following result: if R is a strongly nil Γ-ring satisfying the ascending chain condition on principal left annihilators, then R is a Baer's radical Γ-ring.
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