For a left Noetherian ring R, if the supremum of flat dimensions of all injective left R-modules is finite, we prove that strongly cotorsion left R-modules coincide with Gorenstein injective modules. Furthermore, if \(\textrm{id}{_{R}R}<\infty \), we describe these two classes of modules as certain right perpendiculars \(\mathscr {D}^{\bot }\), where \(\mathscr {D}\) are the classes of injective modules, modules with finite injective and flat dimension, respectively.

中文翻译：

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Gorenstein 内射模块和强扭曲模块何时重合？

对于左诺特环R ，如果所有单射左R模的平面维数上界是有限的，我们证明强扭曲左R模与 Gorenstein 单射模一致。此外，如果\(\textrm{id}{_{R}R}<\infty \)，我们将这两类模块描述为某些直角垂线\(\mathscr {D}^{\bot }\)，其中\(\mathscr {D}\)是单射模块的类，分别是具有有限单射和平维的模块。