What can be said about the characteristic of a ring R in which x=-x for each x in R?
Thank You
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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.Quote:
Originally Posted by hercules
The charachteristic is 2. Because ifQuote:
Originally Posted by hercules
in particular
.
Why did you pick 1 for x value specifically? (where 2x=0)Quote:
Originally Posted by ThePerfectHackerThe charachteristic is 2. Because if
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.Quote:
Originally Posted by hercules
TPH is right. To supplement his comments, read the paragraph right under the definition of the characteristic in your textQuote:
Originally Posted by hercules
Quote:
Originally Posted by Jhevon
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 relevantQuote:
Originally Posted by hercules
I believe field characheristics are only defined for commutative unitary rings.Quote:
Originally Posted by hercules