Abstract A commutative integral domain is primary if and only if it is one-dimensional and local. A domain is strongly primary if and only if it is local and each nonzero principal ideal contains a power of the maximal ideal. Hence, one-dimensional local Mori domains are strongly primary. We prove among other results that if R is a domain such that the conductor vanishes, then is finite; that is, there exists a positive integer k such that each nonzero nonunit of R is a product of at most k irreducible elements. Using this result, we obtain that every strongly primary domain is locally tame, and that a domain R is globally tame if and only if In particular, we answer Problem 38 of the open problem list by Cahen et al. in the affirmative. Many of our results are formulated for monoids.

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关于强初级幺半群和域

摘要 可交换积分域是主域当且仅当它是一维局部的。当且仅当域是局部域且每个非零主理想都包含最大理想的幂时，域才是强主域。因此，一维局部 Mori 域是非常重要的。我们证明了在其他结果中，如果 R 是一个域使得导体消失，那么它是有限的；也就是说，存在一个正整数 k，使得 R 的每个非零非单位是至多 k 个不可约元素的乘积。使用这个结果，我们得到每个强主域都是本地驯服的，并且域 R 是全局驯服的当且仅当特别是，我们回答了 Cahen 等人的开放问题列表的问题 38。是肯定的。我们的许多结果都是为幺半群制定的。