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Thread: Ring problem

  1. #1
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    Ring problem

    Hi there, I need help with this problem. I really dont know what to make of it.

    If R is a ring where x^6=x, (V) x in R.
    a) Is it true that x^5=x ?
    b) 1 + 1 = ?

    Thank you.
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  2. #2
    MHF Contributor

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    Quote Originally Posted by sillyme View Post

    If R is a ring where $\displaystyle x^6=x, \ \forall x \in R.$

    a) Is it true that $\displaystyle x^5=x$? did you mean $\displaystyle x^5 = 1$?

    b) 1 + 1 = ?
    $\displaystyle 1=(-1)^6=-1.$ thus in R: $\displaystyle 1+1=0.$
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