论文标题
关于派生的完整模块和复合物的评论
Remarks on derived complete modules and complexes
论文作者
论文摘要
让$ r $为换圈，$ i \ subset r $有限生成的理想。我们讨论了出现在文献中的$ r $ modules的衍生$ i $ $ $ $ $ $完整（也是衍生的$ i $ torsion）复合物的两个定义：理想主义和顺序的文献中。已知这两个定义相当于弱质观的理想$ i $；我们表明它们不同否则。我们认为顺序方法效果很好，但是理想主义的方法需要重新解释或正确理解。我们还考虑了$ i $ - 原始的flat $ r $ - 模型。
Let $R$ be a commutative ring and $I\subset R$ a finitely generated ideal. We discuss two definitions of derived $I$-adically complete (also derived $I$-torsion) complexes of $R$-modules which appear in the literature: the idealistic and the sequential one. The two definitions are known to be equivalent for a weakly proregular ideal $I$; we show that they are different otherwise. We argue that the sequential approach works well, but the idealistic one needs to be reinterpreted or properly understood. We also consider $I$-adically flat $R$-modules.
