In this paper we are concerned with a long-standing conjecture of Huneke and Wiegand. We introduce a new class of ideals and prove that each ideal from such class satisfies the conclusion of the conjecture in question. We also study the relation between the class of Burch ideals and that of the ideals we define, and construct several examples that corroborate our results.

中文翻译：

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关于一类伯奇理想以及胡内克和韦根的猜想

在本文中，我们关注Huneke和Wiegand的长期猜想。我们介绍了一个新的理想类别，并证明该类别中的每个理想都满足有关猜想的结论。我们还研究了Burch理想的类别与我们定义的理想的类别之间的关系，并构建了一些实例来证实我们的结果。