Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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 ($f+e,g)=(f,g)$?

share|improve this question
add comment

2 Answers

Of course $e$ is also a pair, $e=(e_1,e_2)$. What can you conclude from $(f,g)+(e_1,e_2)=(f,g)$?

share|improve this answer
add comment

Assuming $B$ is a group, it has an identity element $e$. In $B \times B$, therefore $$ (f,g) + (e,e) = (f + e, g + e) = (f,g) $$ for any elements $f$ and $g$, so $(e,e)$ is the identity in $B \times B$.

share|improve this answer
    
this means that e=0 right? –  Youmath Dec 1 '12 at 19:05
    
You don't determine what $e$ is. $e$ is supposed to be the identity element of $B$ with respect to addition. By this calculation $(e,e)$ is the identity in $B \times B$. –  Hans Giebenrath Dec 1 '12 at 19:11
    
@Youmath If by "$0$" you mean "the identity element of $B$ with respect to addition", then yes. You want to be careful with that terminology, however. The group $B$ could be strange and not have an element called "$0$". It might not have any numbers at all. –  Austin Mohr Dec 1 '12 at 19:27
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.