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 which is often written . What are the subrings of this ring and might any of them have the desired property?


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