论文标题
投影性的核芯戈伦斯坦平坦和丁射射击模块
Projectively coresolved Gorenstein flat and Ding projective modules
论文作者
论文摘要
我们提供了必要和足够的条件，以便为投影固定的Gorenstein Flat模块，$ \ Mathcal {pgf} $（分别分别为项目固定的Gorenstein $ \ Mathcal {b} $ flat flat flat flat flat flat {投影模块（$ \ Mathcal {dp}）$。我们证明$ \ Mathcal {pgf} = \ Mathcal {dp} $，并且仅当每个Ding投射模块都是Gorenstein平坦的。例如，如果环$ r $连贯，就是这种情况。我们包括一个示例，以表明连贯性是足够的，但不是必需的条件，以便拥有$ \ Mathcal {pgf} = \ Mathcal {dp} $。我们还表明，$ \ Mathcal {pgf} = \ Mathcal {dp} $上的任何环$ r $的有限弱Gorenstein Global Dimension（此条件也足够，但不是必需的）。我们证明，如果Ding投影模块的类别（$ \ Mathcal {dp} $）正在覆盖，那么RING $ R $是完美的。我们表明，在连贯的环$ r $上，匡威也保持着。我们还提供了必要和足够的条件，以便拥有$ \ Mathcal {pgf} = \ Mathcal {gp} $，其中$ \ Mathcal {gp} $是Gorenstein Projective模块的类。
We give necessary and sufficient conditions in order for the class of projectively coresolved Gorenstein flat modules, $\mathcal{PGF}$, (respectively that of projectively coresolved Gorenstein $\mathcal{B}$ flat modules, $\mathcal{PGF}_{\mathcal{B}}$) to coincide with the class of Ding projective modules ($\mathcal{DP})$. We show that $\mathcal{PGF} = \mathcal{DP}$ if and only if every Ding projective module is Gorenstein flat. This is the case if the ring $R$ is coherent for example. We include an example to show that the coherence is a sufficient, but not a necessary condition in order to have $\mathcal{PGF} = \mathcal{DP}$. We also show that $\mathcal{PGF} = \mathcal{DP}$ over any ring $R$ of finite weak Gorenstein global dimension (this condition is also sufficient, but not necessary). We prove that if the class of Ding projective modules, $\mathcal{DP}$, is covering then the ring $R$ is perfect. And we show that, over a coherent ring $R$, the converse also holds. We also give necessary and sufficient conditions in order to have $\mathcal{PGF} = \mathcal{GP}$, where $\mathcal{GP}$ is the class of Gorenstein projective modules.
