Proving the identity of the field

  • Thread starter Thread starter playa007
  • Start date Start date
  • Tags Tags
    Field Identity
playa007
Messages
25
Reaction score
0

Homework Statement


If S = {s in R such that s=/=1} is an abelian group under circle operation (Circle Operation a*b = a + b -ab for a, b in R) then R is a field

Homework Equations


The verification of the field axioms

The Attempt at a Solution


The field axiom that I'm struggling to verify is the existence of the identity for the multiplicative operation since s=/=1. I'm wondering if someone can help me resolve this.

Thanks
 
Physics news on Phys.org
Isn't the identity 0? Why do you think it's not?
 
If aob= a+ b- ab Then the identity, e, must satisfy a+ e+ ae= a for all a. Solve that for e.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Prove ##a \cdot 1 = a = 1 \cdot a## for ##a \in \mathbb{N}##
Replies
1
Views
1K
Prove ##1 + a=s(a)=a+1## for ##a \in \mathbb{N}##
Replies
1
Views
1K
Prove ##(a+b)\cdot c=a\cdot c+b\cdot c## using Peano postulates
Replies
3
Views
1K
Prove ##a\cdot b = b \cdot a ##using Peano postulates
Replies
3
Views
1K
Prove if ##a\cdot c = b \cdot c## then ##a = b## using Peano postulates
Replies
2
Views
1K
Prove ##(a\cdot b)\cdot c =a\cdot (b \cdot c)## using Peano postulates
Replies
1
Views
1K
Proving Closure and Identity for U(n)
Replies
16
Views
4K
Prove ##a + b = b + a## using Peano postulates
Replies
3
Views
1K
Show GL/O/SO(n,R) form groups under Matrix Multiplication
Replies
2
Views
2K
Determining a group, by checking the group axioms
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top