具有强对称自同态的环及其扩张

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.

Rings with Strongly Symmetric Endomorphisms and Their Extensions

The rings with strongly symmetric endomorphisms were investigated. Let α be an endomorphism of ring R. Ring R is known as strong right α-symmetric if abα(c)=0 implies acb=0 for any a,b,c∈R. The relationships between strong α-symmetric ring and symmetric, strong α-reversible or strong α-semicommutative ring were discussed, and some extensions of strong α-symmetric rings were st
udied. It is proved that 1) Ring R is strong α-symmetric if and onlyif R is symmetric and α-compatible; 2) Ring R is strong α-symmetric if and only if R［x;α］ is strong α-symmetric; 3) If α is an automorphism of right Ore ring R, then R is strong α-symmetric if and only if the classical right quotient ring Q(R) of R is strongα-symmetric.