Show that the ring is commutative

Asked Sep 02 '20 at 12:00

Active Sep 04 '20 at 13:02

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$$R\textrm{ is a ring(multiplicative identity not assumed) such that }x^{3}=x \: \: \forall x\in R.\\ \textrm{Prove that }R\textrm{ is a commutative ring }.$$

I have been able to show that $6x=0$ for all $x$ in $R$. Can I get some hints on how to proceed?

edited Sep 04 '20 at 13:02

Alessio K

10,679

asked Sep 02 '20 at 12:00

tony

2

See https://math.stackexchange.com/questions/67148/if-a3-a-for-all-a-in-a-ring-r-then-r-is-commutative – Angina Seng Sep 02 '20 at 12:03
thanks. will check it out – tony Sep 02 '20 at 12:08

Show that the ring is commutative

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