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 August 25th, 2010, 10:45 AM #1 Newbie   Joined: Aug 2010 Posts: 3 Thanks: 0 Ring Give an example of a non trivial commutative ring in which every element is of square 0
 August 25th, 2010, 12:27 PM #2 Senior Member   Joined: Aug 2010 Posts: 195 Thanks: 5 Re: Ring Does your definition of a ring include a multiplicative identity? If so, can this multiplicative identity ever square to zero?
 August 26th, 2010, 09:45 AM #3 Newbie   Joined: Aug 2010 Posts: 3 Thanks: 0 Re: Ring No there is no mulplicative identity 1
 August 26th, 2010, 08:28 PM #4 Senior Member   Joined: Aug 2010 Posts: 195 Thanks: 5 Re: Ring Then what are the subrings of the integers mod 4? Do any of them have this property?
 August 29th, 2010, 06:49 PM #5 Newbie   Joined: Aug 2010 Posts: 3 Thanks: 0 Re: Ring Do you mean the subrings of Z_4
 August 29th, 2010, 08:53 PM #6 Senior Member   Joined: Aug 2010 Posts: 195 Thanks: 5 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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