幂零p.p.-环和幂零Baer环的Ore扩张

On Ore extensions of nilpotent p. p.-rings and nilpotent Baer rings

研究环的Ore扩张的幂零p.p.性,幂零Baer性和弱Mc Coy性,主要证明了:设R是一个拟IFP和(α,δ)-condition环,则有(1)如果R是幂零p.p.-环,则R[x;α,δ]是幂零p.p.-环;(2)如果R是幂零Baer环,则R[x;α,δ]是幂零Baer环;(3)R[x;α,δ]是右弱M c Coy环。

The nilpotent p. p.,nilpotent Baer and weak M c Coy property of the Ore extensions of a ring are investigated. Let R be a quasi-IFP and（ α,δ）-condition ring. It is mainly shown that（ 1） if R is a nilpotent p. p.-ring,then R[x; α,δ] is a nilpotent p. p.-ring;（ 2） if R is a nilpotent Baer ring,then R[x; α,δ] is a nilpotent Baer ring;（ 3）R[x; α,δ] is a weak M c Coy ring.