Examples for regular ideals in commutative rings

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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?

thank you