论文标题
减少和成芯模块I的应用I
Applications of reduced and coreduced modules I
论文作者
论文摘要
这是一系列论文中的第一篇，突出了还原和核述模块的应用。让$ r $为换向的Unital环，而$ i $是$ r $的理想。我们表明，$ i $ rduced $ r $ - 模块和$ i $ corecucts $ r $ - 模块提供了一个设置，其中Matlis-Greenless-May（MGM）等价和无绿色 - 杂货（GM）二元性持有。迄今为止，这两个概念仅在派生类别设置中存在。我们意识到$ i $ torsion和$ i $ aidic完成函数是代表函数，在适当的条件下，可以计算它们与其他函数之间的自然转换。
This is the first in a series of papers highlighting the applications of reduced and coreduced modules. Let $R$ be a commutative unital ring and $I$ an ideal of $R$. We show that $I$-reduced $R$-modules and $I$-coreduced $R$-modules provide a setting in which the Matlis-Greenless-May (MGM) Equivalence and the Greenless-May (GM) Duality hold. These two notions have been hitherto only known to exist in the derived category setting. We realise the $I$-torsion and the $I$-adic completion functors as representable functors and under suitable conditions compute natural transformations between them and other functors.
