On -Power Conductor domains [article]

Daniel D. Anderson, Evan Houston, Muhammad Zafrullah
<span title="2017-10-17">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Let D be an integral domain and a star operation defined on D. We say that D is a -power conductor domain ( -PCD) if for each pair a,b∈ D (0) and for each positive integer n we have Da^n∩ Db^n=((Da∩ Db)^n)^∗. We study -PCDs and characterize them as root closed domains satisfying ((a,b)^n)^-1=(((a,b)^-1)^n)^ for all nonzero a,b and all natural numbers n≥ 1. From this it follows easily that Prüfer domains are d-PCDs (where d denotes the trivial star operation), and v -domains (e.g., Krull
more &raquo; ... are v-PCDs, thereby establishing that a v -domain (e.g., a Prufer or Krull domain) is a -PCD. We also consider when a -PCD is completely integrally closed, and this leads to new characterizations of Krulll domains. In particular, we show that a Noetherian domain is a Krull domain if and only if it is a w -PCD.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1710.06521v1">arXiv:1710.06521v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/s43kqgllejfebeqhvrok7lqykq">fatcat:s43kqgllejfebeqhvrok7lqykq</a> </span>
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