幂零元的单边零可交换性

One-sided Commutativity of Nilpotent Elements at Zero

定义研究左和右幂零可逆环,这两类环与可逆环的单边幂零结构密切相关,是CNZ环的一个真子类。证明环R是可逆环当且仅当R是半素的左幂零可逆环。研究左幂零可逆环的扩张性质,主要证明了以下结果:R是左幂零可逆环当且仅当A(R,α)是左幂零可逆环;Armendariz环R是左幂零可逆环当且仅当R[x]是左幂零可逆环;若右Ore环R是左幂零可逆的,则R的经典右商环Q是左幂零可逆的。

The concepts of left and right nilpotent reversible rings are defined and studied,which are closely related to the one-sided nilpotent structures of reversible rings,and are a proper subclass of CNZ rings.It is shown that a ring R is reversible if and only if R is semiprime and left nilpotent reversible ring.Various extension properties of left nilpotent reversible rings are studied,the following results are mainly proved:Aring R is left nilpotent reversible if and only if A(R,α)is left nilpotent reversible.If R is an Armendariz ring,then R is left nilpotent reversible if and only if R[x]is left nilpotent reversible.If a right Ore ring R is a left nilpotent reversible ring,then its classical right quotient ring Q is left nilpotent reversible.