- #1
tc_11
- 8
- 0
Hi, I found a couple of proofs proving that 1=0 only in the trivial ring {0}. They say
Suppose 1 = 0. Let a be any element in R; then a = a ⋅ 1 = a ⋅ 0 = 0.
But what I don't understand is that they say a = a ⋅ 1. But that is only true if a ring has unity (x*1=1*x=x), and it is possible to have a ring without unity, so why is it okay to say a = a ⋅ 1?
Suppose 1 = 0. Let a be any element in R; then a = a ⋅ 1 = a ⋅ 0 = 0.
But what I don't understand is that they say a = a ⋅ 1. But that is only true if a ring has unity (x*1=1*x=x), and it is possible to have a ring without unity, so why is it okay to say a = a ⋅ 1?