吉林大学学报（理学版）Issue(5)：861-868,8.DOI:10.13413/j.cnki.jdxblxb.2014.05.01
具有强对称自同态的环及其扩张
Rings with Strongly Symmetric Endomorphisms and Their Extensions
摘要
Abstract
The rings with strongly symmetric endomorphisms were investigated. Let α be an endomorphism of ring R.Ring R is known as strong rightα-symmetric if abα(c)=0 implies acb=0 for any a,b,c∈R.The relationships between strongα-symmetric ring and symmetric,strongα-reversible or strongα-semicommutative ring were discussed,and some extensions of strongα-symmetric rings were studied.It is proved that 1 )Ring R is strongα-symmetric if and only if R is symmetric andα-compatible;2)Ring R is strongα-symmetric if and only if R[x;α]is strongα-symmetric;3)Ifαis an automorphism of right Ore ring R,then R is strongα-symmetric if and only if the classical right quotient ring Q(R)of R is strongα-symmetric.关键词
强α-对称环/强α-可逆环/强α-半交换环/α-compatible环/经典右商环/斜多项式环Key words
strongα-symmetric ring/strongα-reversible ring/strongα-semicommutative ring/α-compatible ring/classical right quotient ring/skew polynomial ring分类
数理科学引用本文复制引用
王尧,薛岭,任艳丽..具有强对称自同态的环及其扩张[J].吉林大学学报（理学版）,2014,(5):861-868,8.基金项目
国家自然科学基金(批准号:11101217)和江苏省自然科学基金(批准号:BK20141476) （批准号:11101217）
