Abstract In this article, a new semistar operation, called the q-operation, on a commutative ring R is introduced in terms of the ring of finite fractions. It is defined as the map by there exists some finitely generated semiregular ideal J of R such that for any where denotes the set of nonzero R-submodules of The main superiority of this semistar operation is that it can also act on R-modules. We can also get a new hereditary torsion theory τq induced by a (Gabriel) topology is an ideal of R with Based on the existing literature of τq-Noetherian rings by Golan and Bland et al., in terms of the q-operation, we can study them in more detailed and deep module-theoretic point of view, such as τq-analog of the Hilbert basis theorem, Krull’s principal ideal theorem, Cartan-Eilenberg-Bass theorem, and Krull intersection theorem.

中文翻译：

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交换环上一种新的半星运算及其应用

摘要 在本文中，根据有限分数环，在交换环 R 上引入了一种新的半星运算，称为 q 运算。它被定义为映射，存在一些有限生成的 R 的半正则理想 J 使得对于任何 表示非零 R 子模的集合 这种半星运算的主要优点是它也可以作用于 R 模。我们还可以得到一个新的遗传扭转理论 τq 由（Gabriel）拓扑引起的 R 的理想基于 Golan 和 Bland 等人关于 τq-Noetherian 环的现有文献，在 q 操作方面，我们可以从更详细、更深入的模理论的角度来研究它们，例如希尔伯特基定理的τq-analog、Krull 主理想定理、Cartan-Eilenberg-Bass 定理和Krull 交集定理。