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 Mathew August 25th, 2010 10:45 AM

Ring

Give an example of a non trivial commutative ring in which every element is of square 0

 Turgul August 25th, 2010 12:27 PM

Re: Ring

Does your definition of a ring include a multiplicative identity? If so, can this multiplicative identity ever square to zero?

 Mathew August 26th, 2010 09:45 AM

Re: Ring

No there is no mulplicative identity 1

 Turgul August 26th, 2010 08:28 PM

Re: Ring

Then what are the subrings of the integers mod 4? Do any of them have this property?

 Mathew August 29th, 2010 06:49 PM

Re: Ring

Do you mean the subrings of Z_4

 Turgul August 29th, 2010 08:53 PM

Re: Ring

Yes, I mean $\mathbb{Z}/4\mathbb{Z}$ which is often written $\mathbb{Z}_4$. What are the subrings of this ring and might any of them have the desired property?

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