一类结合环的交换性

目的证明满足一定条件的结合环的交换性。方法在以往研究满足一定条件结合环之交换性的思路和方法的基础上,根据结合环的交换性定理,给出了通过环论用演绎法证明的方法。结果设R为结合环,如果R满足条件:(i)R有单位元1;(ii)R无幂零指数为2的非零幂零元;(iii)对任意x,y∈R,均有依赖于x,y的正整数n=n(x,y)使得xyn-ynx∈C,xyn+1-yn+1x∈C,此处C为环R的中心,则R为交换环。结论当结合环满足一定条件时具有交换性。

Commutativity of a class of associative rings

Aim To demonstrate the commutativity of the associative ring that satisfies a certain condition.Methods On the basis of the previous research thinking and methods of commutativity of the associative rings under certain condition,the approach is given with deductive method in ring theory in line with commutativity theorem of associative rings.Results Let R be an associative ring,if R satisfies the following conditions:(i) R has a unit;(ii) R doesn't have such a nonzero nilpotent element whose nilpotent expon...