%0 Journal Article
%T (α,δ)-弱刚性环上的Ore扩张<br>ORE EXTENSIONS OVER (α,δ)-WEAKLY RIGID RINGS
%A 作者
%A 王尧
%A 张玖琳
%A 任艳丽
%J 数学杂志
%D 2017
%X 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.<br>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
%K (α
%K δ)-弱刚性环 Ore扩张 弱对称环 弱zip环 幂零p.p.环 幂零Baer环&lt
%K br&gt
%K (α
%K δ)-weakly rigid ring Ore extension weak symmetric ring weak zip ring nilpotent p.p.-ring nilpotent Baer ring
%U http://sxzz.whu.edu.cn/sxzz/ch/reader/view_abstract.aspx?file_no=20170322&flag=1