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August 25th, 2010, 10:45 AM   #1
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Ring

Give an example of a non trivial commutative ring in which every element is of square 0
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August 25th, 2010, 12:27 PM   #2
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Re: Ring

Does your definition of a ring include a multiplicative identity? If so, can this multiplicative identity ever square to zero?
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August 26th, 2010, 09:45 AM   #3
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Re: Ring

No there is no mulplicative identity 1
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August 26th, 2010, 08:28 PM   #4
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Re: Ring

Then what are the subrings of the integers mod 4? Do any of them have this property?
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August 29th, 2010, 06:49 PM   #5
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Re: Ring

Do you mean the subrings of Z_4
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August 29th, 2010, 08:53 PM   #6
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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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