  We study the two dual notions of prime avoidance and prime absorbance. We
generalize the classical prime avoidance lemma to radical ideals. A number of
new criteria are provided for an abstract ring to be C.P. (every set of primes
satisfies avoidance) or P.Z. (every set of primes satisfies absorbance).
Special consideration is given to the interaction with chain conditions and
Noetherian-like properties. It is shown that a ring is both C.P. and P.Z. iff
it has finite spectrum.
