We have the Cartesian product $B \times B$ and there we have the addition $$(f,g)+(h,k)=(f+h,g+k)$$ and the multiplication $$(f,g) \cdot (h,k)=(f\cdot h+g\cdot k,f\cdot k+g\cdot h).$$ I want to find the identity element of the group related to the addition. So I must have something like $(f,g)+e=(f,g)$. What do I do now? Is it something like ($f+e,g)=(f,g)$?
Ring theory question please?Simple.
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ring-theory