Generating Rings with Ideals: The Possibilities and Implications

[Simfish]

Do all rings have to be generated by ideals? Or can some rings come without ideals?

Can some elements in rings be generated by ideals (in ways that other elements of rings are untouched by ideals?)

If ALL of a ring's elements are generated by ideals, is there something special about the ring? (for example, the ring of Gaussian integers is completely generated by around 6 ideals IIRC).

If an element in a ring is hit on by two different ideals, is there anything wrong with that?

 

[ircdan]

every ring R always has 2 ideals, namely {0} and R

i don't understand your other questions

 

[Emmanuel114]

No proper ideals = Simple rings.

If I remember correctly, if an ideal contains 1, then that ideal generates the ring or something like that.

Can't think of anything else at this hour.