# commutative ring satisfying descending chain condition on radical ideals

Let $$R$$ be a commutative ring with unity which satisfies d.c.c. on radical ideals. then does $$R$$ satisfy a.c.c. on radical ideals ? If this is not true in general, then what happens if we also assume $$R$$ is a local domain and/or that $$R$$ has finite Krull dimension ?

NOTE: If $$R$$ has finite Krull dimension, then obviously $$R$$ satisfies a.c.c. on prime ideals.

By the answer below of David Lampert, it follows that only assuming local domain is not enough to guarantee a.c.c. on radical ideals.