Govorov-Lazard定理的无Gorenstein模拟的环
Rings without a Gorenstein analogue of the Govorov-Lazard Theorem
摘要：
Bkillannis和Krause证明了在某些Artin代数上存在Gorenstein平坦模，它们不是生成Gorenstein投射模的直接极限.也就是说，这些代数没有Gorenstein类似的Govorov-Lazard定理。我们表明，事实上，有一大类环没有这样的模拟。设R是交换局部诺特环.则R的类似物失败，如果它有一个对偶复形，是亨泽尔的，而不是Gorenstein的，并有一个非自由生成的Gorenstein投射模。证明是基于Gorenstein投影（前）信封的理论。我们表明，除其他事项外，在modR的生成Gorenstein投射模形成一个包络类当且仅当R是Gorenstein或具有的属性，每个生成Gorenstein投射模是免费的。这与最近Christensen、Piepmeyer、Striuli和Takahashi关于封面的结果类似，他们的方法对我们的工作是一个重要的输入。
英文摘要：
It was proved by Beligiannis and Krause that over certain Artin algebras, there are Gorenstein flat modules which are not direct limits of finitely generated Gorenstein projective modules. That is, these algebras have no Gorenstein analogue of the Govorov-Lazard Theorem. We show that, in fact, there is a large class of rings without such an analogue. Namely, let R be a commutative local noetherian ring. Then the analogue fails for R if it has a dualizing complex, is henselian, not Gorenstein, and has a finitely generated Gorenstein projective module which is not free. The proof is based on a theory of Gorenstein projective (pre)envelopes. We show, among other things, that the finitely generated Gorenstein projective modules form an enveloping class in mod R if and only if R is Gorenstein or has the property that each finitely generated Gorenstein projective module is free. This is analogous to a recent result on covers by Christensen, Piepmeyer, Striuli, and Takahashi, and their methods are an important input to our work.
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