(α,δ)-弱刚性环上的Ore扩张
ORE EXTENSIONS OVER (α,δ)-WEAKLY RIGID RINGS

本文研究（α，δ）-弱刚性环上的Ore扩张环R[x；α，δ]的弱对称性、弱zip性、幂零p.p.性和幂零Baer性.利用对多项式的逐项分析的方法，证明了如果R是（α，δ）-弱刚性环和半交换环，则Ore扩张环R[x；α，δ]是弱对称的（弱zip的，幂零p.p.的，幂零Baer的）当且仅当R是弱对称的（弱zip的，幂零p.p.的，幂零Baer的）.这些结果统一和扩展了前面已有的相关结论.
In this paper, we investigate the weak symmetric, weak zip, nilpotent p.p. and nilpotent Baer property of the Ore extension R[x; α,δ] of a ring R, respectively. By using the itemized analysis method on polynomials, we prove that if R is (α,δ)-weakly rigid and semicommutative, then R[x; α,δ] is weak symmetric (resp., weak zip, nilpotent p.p., nilpotent Baer) if and only if R is weak symmetric (resp., weak zip, nilpotent p.p., nilpotent Baer). These results unify and extend nontrivially the previously known results