结合环的交换性条件

Commutativity of Associative Rings

证明了满足下列条件的Kothe半单纯环为交换环:如果对R中任意元y,有依于y的非负整数m(y),n(y),s(y),t(y)及fy(y),在y2Z[Y]中使得xmyxn-xsf(y)xt与x的换位子在Z[R]中对一切的R中元x成立.

In this paper, Kothe semi-simple ring is proved to be commutative rings if it satisfies the following conditions: if for any y∈R, nonnegative integers m(y), n(y), s(y), t(y) and fy(y) ∈y2Z[Y]exist, so xmyxn-x3f(y)xt and x commutator owning to Z[R] for all x.