Avoidance and absorbance

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