Abstract Let R be a commutative ring with identity and the set of regular height one prime ideals of R. We will show that R is a Krull ring if and only if each regular prime ideal of R contains a t-invertible prime ideal, if and only if (1) and it has finite character and (2) is a rank one DVR for each It is also shown that is the unique defining family for a Krull ring R.

中文翻译：

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关于具有零除数的 Krull 环

摘要 令 R 为具有恒等式和 R 的规则高度为一素理想的集合的交换环。 我们将证明 R 是 Krull 环当且仅当 R 的每个规则素理想都包含一个 t-可逆素理想，如果且仅当 (1) 并且它具有有限的特征并且 (2) 是每个的一级 DVR 还表明它是 Krull 环 R 的唯一定义族。