论文标题
最小的淤泥模块和环扩展
Minimal silting modules and ring extensions
论文作者
论文摘要
环的表达通常会诱导淤泥模块和固定模块，称为最小的淤积或最小的旋转。本文的目的是双重的。首先，我们确定在驯服的世袭代数上的最小倾斜和最小的插入模块。特别是，我们表明，当它具有直接汇总时，只有当它具有ADIC模块时，一个大的插座模块是最小的。其次，我们讨论了环扩展下最小值的行为。我们表明，沿着任何平坦环的表达式延伸到最小的固定环模块上的最小固定模块。对于较小同源维度的交换环获得了类似的结果。
Ring epimorphisms often induce silting modules and cosilting modules, termed minimal silting or minimal cosilting. The aim of this paper is twofold. Firstly, we determine the minimal tilting and minimal cotilting modules over a tame hereditary algebra. In particular, we show that a large cotilting module is minimal if and only if it has an adic module as a direct summand. Secondly, we discuss the behaviour of minimality under ring extensions. We show that minimal cosilting modules over a commutative noetherian ring extend to minimal cosilting modules along any flat ring epimorphism. Similar results are obtained for commutative rings of small homological dimension.
