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 compactly packed (C.P., every set of primes satisfies avoidance) or properly zipped (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. if and only if it has finite prime spectrum.

中文翻译：

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回避和吸收

我们研究了主要规避和主要吸收的两个双重概念。我们将经典的主要回避引理推广为激进的理想。为紧凑包装（CP，每组素数都满足避免）或适当压缩（PZ，每组素数均满足吸收性）提供了抽象环的许多新标准。特别考虑了与链条条件和Noetherian型性质的相互作用。结果表明，当且仅当环具有有限的本征谱时，环才是CP和PZ。