论文标题
模块类别中的最大解构性
Maximum deconstructibility in module categories
论文作者
论文摘要
我们证明，Vopěnka的原理意味着对于每个戒指上的模块的$ \ mathfrak {x} $，\ textbf {$ \ boldsymbol {\ boldsymbol {\ mathfrak {x x}}} $ - gorenstein Projective Modules} $ （\ textbf {$ \ boldsymbol {\ mathfrak {x}} $ - $ \ boldsymbol {\ mathcal {gp}} $} $} $}）是一个特殊的重跨类。特别是，不可能证明（除非vopěnka的原则是不一致的），即有一个环\ textbf {ding projectives}（$ \ boldsymbol {\ boldsymbol {\ nathcal {dp}}} $）或\ textbf {gorenstein projectives} $ \ boldsymbol {形成一个重新覆盖的类（šaroch以前使用不同的方法为类$ \ Mathcal {gp} $获得了此结果）。关键创新是\ emph {deNstructibility}的一种新的“自上而下”表征，这是一个众所周知的足够条件。我们还证明，Vopěnka的原理在某种意义上意味着模块类别中最大可能的解构性量。
We prove that Vopěnka's Principle implies that for every class $\mathfrak{X}$ of modules over any ring, the class of \textbf{$\boldsymbol{\mathfrak{X}}$-Gorenstein Projective modules} (\textbf{$\boldsymbol{\mathfrak{X}}$-$\boldsymbol{\mathcal{GP}}$}) is a special precovering class. In particular, it is not possible to prove (unless Vopěnka's Principle is inconsistent) that there is a ring over which the \textbf{Ding Projectives} ($\boldsymbol{\mathcal{DP}}$) or the \textbf{Gorenstein Projectives} ($\boldsymbol{\mathcal{GP}}$) do not form a precovering class (Šaroch previously obtained this result for the class $\mathcal{GP}$, using different methods). The key innovation is a new "top-down" characterization of \emph{deconstructibility}, which is a well-known sufficient condition for a class to be precovering. We also prove that Vopěnka's Principle implies, in some sense, the maximum possible amount of deconstructibility in module categories.
