Prove that if in a ring R, x^3=x for all x in R, then ring R is commutative.

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  1. Maths ICU
  2. conjugate of a number
  3. complex numbers
  4. conjugate
  5. complex analysis
  6. real analysis
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Комментарии
Автор

If x^2=0 for some x in a ring R and x^3=x for every x in R, then x=x^3=x.x^2=x.0=0.

MathsICU
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wonderful sir smj aa gya ❤❤ apka awaz acha hai 😊

vansh
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Can we prove it using one-one onto, polynomial ring?

DescryGames
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at 9:00, we have used the property a + (-a) =0, as R is a group with respect to +. (Not the cancellation laws.)

MathsICU
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At 19:00 why cant we replace x^2 by x-x^2 directly as x^2 can be anything.

lost
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Where does (x^2y - x^2yx^2)^2 come from?
Can I just make up anything that will help match up x^3 = x, or is that expression something I should already know?

MrHolmes
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What will happen if (x²y-x²yx²) become divisor of zero ?
Can we then write (x²y-x²yx²)²=0 => (x²y-x²yx²)=0 ???

nawazsarif