Rings are commutative with 1.
Definition. A regular ideal refers to an ideal containing a non-zero-divisor.
I can easily build ideals which are not regular. but what about regular ideals?
I know trivial ones:
1- A ring $R$ has at least one regular ideal, $R$ itself. 2- In an integral domain nonzero ideal is regular.
How can I build other (non-trivial) ones?