Tensor product of modules over non commutative rings
I have a problem on operation, since I am the beginner, I am confused whether the subgroup K generated by one of generator $(x_1+x_2,y)-(x_1,y)-(x_2,y)$, cannot simply to $(0,-y)$(ie pointwise) does it is not direct product? thanks a lot
if you have any misunderstanding, please tell me