中文摘要：

设α为环R的自同态,如果对任意的a,b,c∈R,由abα（c）=0可推出acb=0,则称R是强右α-对称环。研究强α-对称环与对称环、强α-可逆环、强α-半交换环等相关环的关系及强α-对称环的扩张性质,证明了：1）环R是强α-对称环当且仅当R是对称环且是α-compatible环；2）设R是约化环,则R是强α-对称环当且仅当R[x；α]是强α-对称环；3）设α是右Ore环R的自同构,则环R是强α-对称环当且仅当Q（R）是强α-对称环。

英文摘要：

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.