August 25th, 2010, 11:45 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, 01:27 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, 10:45 AM  #3 
Newbie Joined: Aug 2010 Posts: 3 Thanks: 0  Re: Ring
No there is no mulplicative identity 1

August 26th, 2010, 09:28 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, 07:49 PM  #5 
Newbie Joined: Aug 2010 Posts: 3 Thanks: 0  Re: Ring
Do you mean the subrings of Z_4

August 29th, 2010, 09:53 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?


Tags 
ring 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Ring  sebaflores  Abstract Algebra  1  October 27th, 2013 05:29 PM 
ring  tinynerdi  Abstract Algebra  4  April 4th, 2010 11:17 PM 
Ring and pseudoring  cgouttebroze  Abstract Algebra  5  August 14th, 2008 01:04 PM 
ring  stf123  Abstract Algebra  3  December 7th, 2007 08:47 AM 
ring  Frazier001  Abstract Algebra  1  December 6th, 2007 02:21 PM 