戈伦斯坦扁平预封套

Pub Date : 2015-10-01 DOI:10.18910/57638

A. Iacob

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引用次数: 3

摘要

我们考虑一个双面诺瑟环R，使得Gorenstein内射左R-模的特征模是Gorenstein平右R-模。然后证明了Gorenstein平面右r模类是预包络的。我们还证明了右R模的Gorenstein平面配合物在Ch(R)中是预先发展的。在本文的第二部分，我们给出了一些环的例子，这些环具有Gorenstein内射模的特征模是G或nstein平的性质。证明了任意边noether环R < 1具有期望性质。我们还证明了ifR是一个具有对偶双模RVR的双面诺瑟环，且对于某正整数n, r是左n-完全的，则Gorenstein内射模的特征模是Gorenstein平的。

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Gorenstein Flat Preenvelopes

We consider a two sided noetherian ring R such that the character modules of Gorenstein injective leftR-modules are Gorenstein flat right R-modules. We then prove that the class of Gorenstein flat right R-modules is preenveloping. We also show that the class of Gorenstein flat complexes of right R-modules is preenevloping in Ch(R). In the second part of the paper we give examples of rings with t he property that the character modules of Gorenstein injective modules are G or nstein flat. We prove that any two sided noetherian ring R with i.d.Rop R < 1 has the desired property. We also prove that ifR is a two sided noetherian ring with a dualizing bimodule RVR and such thatR is left n-perfect for some positive integer n, then the character modules of Gorenstein injective modules are Gorenstein flat .

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