About characteristic of rings

• April 12th 2008, 11:52 AM
hercules
About characteristic of rings
What can be said about the characteristic of a ring R in which x=-x for each x in R?

Thank You
• April 12th 2008, 03:56 PM
hercules
i picked up some alien signals
Quote:

Originally Posted by hercules
What can be said about the characteristic of a ring R in which x=-x for each x in R?
Thank You

I think i got it now. But if anyone has any ideas and suggestions...please do post them ....they will help me understand better.
• April 12th 2008, 05:29 PM
ThePerfectHacker
Quote:

Originally Posted by hercules
What can be said about the characteristic of a ring R in which x=-x for each x in R?

Thank You

The charachteristic is 2. Because if $x=-x\implies x + x = 0$ in particular $2\cdot 1 = 0$.
• April 13th 2008, 07:54 AM
hercules
Quote:

Originally Posted by ThePerfectHacker
The charachteristic is 2. Because if $x=-x\implies x + x = 0$ in particular $2\cdot 1 = 0$.

Why did you pick 1 for x value specifically? (where 2x=0)
• April 13th 2008, 07:56 AM
ThePerfectHacker
Quote:

Originally Posted by hercules
Why did you pick 1 for x value specifically? (where 2x=0)

It really works for any value of x. But field charachteristics are defined for 1. Because if 1 + 1 = 0 then it is true for any element. That is why we resrict out attention to 1.
• April 13th 2008, 08:43 AM
Jhevon
Quote:

Originally Posted by hercules
Why did you pick 1 for x value specifically? (where 2x=0)

TPH is right. To supplement his comments, read the paragraph right under the definition of the characteristic in your text
• April 13th 2008, 11:40 AM
hercules
Quote:

Originally Posted by Jhevon
TPH is right. To supplement his comments, read the paragraph right under the definition of the characteristic in your text

Isn't that only if ring has unity?

Don't worry about it ...it just takes me longer to get it but i'll get it.
• April 13th 2008, 06:25 PM
Jhevon
Quote:

Originally Posted by hercules
Isn't that only if ring has unity?

Don't worry about it ...it just takes me longer to get it but i'll get it.

1 is the unity element. otherwise, we have 2x = 0 for all x in R, so either definition is satisfied. I was just trying to show you why considering 1 was relevant
• April 13th 2008, 07:14 PM
ThePerfectHacker
Quote:

Originally Posted by hercules
Isn't that only if ring has unity?

I believe field characheristics are only defined for commutative unitary rings.