Let N be a zero-symmetric prime nearring,got the following results:(ⅰ)If N is 2-torsion-free,d_1 and d_2 are derivatins of N,then the following three conditions are equivalent:(1)d_1d_2 is a derivation;(2)d_1(x)d_2(y)+d_2(x)d_1(y)=0,x,y∈N;(3)either d_1=0 or d_2=0.
设N是零对称的素拟环,证明了:(ⅰ)若N是2-挠自由的,d1,d2是N上的两个导子,则下列3条件等价:(1)d1d2是一个导子;(2)d1(x)d2(y)+d2(x)d1(y)=0,x,y∈N;(3)d1=0或d2=0。
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Let N be a zero-symmetric prime nearring,got the following results:(ⅰ)If N is 2-torsion-free,d_1 and d_2 are derivatins of N,then the following three conditions are equivalent:(1)d_1d_2 is a derivation;(2)d_1(x)d_2(y)+d_2(x)d_1(y)=0,x,y∈N;(3)either d_1=0 or d_2=0.
设N是零对称的素拟环,证明了:(ⅰ)若N是2-挠自由的,d1,d2是N上的两个导子,则下列3条件等价:(1)d1d2是一个导子;(2)d1(x)d2(y)+d2(x)d1(y)=0,x,y∈N;(3)d1=0或d2=0。