Possible Rings with Product of Nonzero Elements Equal to 0?

[helix999]

for which of the following rings is it possible for the product of two nonzero elements to be 0?



1. ring of complex numbers
2. ring of integers modulo 11
3. the ring of continuous real-valued functions on [0,1]
4. the ring {a+b(sqrt(2)) : a & b are rational numbers}
5. ring of polynomials in x with real coefficients

 

[HallsofIvy]

for which of the following rings is it possible for the product of two nonzero elements to be 0?



1. ring of complex numbers
2. ring of integers modulo 11
3. the ring of continuous real-valued functions on [0,1]
4. the ring {a+b(sqrt(2)) : a & b are rational numbers}
5. ring of polynomials in x with real coefficients

What have you done on this yourself? Surely you don't want people to just give you the answers!

 

[helix999]

I have just tried to find out some good online tutorials on Rings. When I think of rings, an empty circle comes to my mind...nothing else. I want to know the explanations of each & every points mentioned above otherwise I wouldn't have written them because I have the correct answer.

 

[helix999]

it is 3rd one