论文标题
相对全球戈伦斯坦维度
Relative global Gorenstein dimensions
论文作者
论文摘要
令$ \ Mathcal {a} $为Abelian类别。在本文中，我们研究了全局$（\ Mathcal {x}，\ Mathcal {y}）$ - Gorenstein投射维度$ \ MATHRM {gl.gpd}（\ Mathcal {x}，\ Mathcal {y Mathcal {y} ，\ Mathcal {y}）$。我们在$（\ Mathcal {x}，\ Mathcal {y}）$上提供同源条件。此外，给定一个gi-Admisible Pair $（\ Mathcal {z}，\ Mathcal {w}）$，我们研究$ \ MATHRM {gl.gid}的条件（\ Mathcal {z}，\ Mathcal {w} $ \ mathrm {gl.gpd}（\ Mathcal {x}，\ Mathcal {y}）（\ Mathcal {a}）$是相同的。
Let $\mathcal{A}$ be an abelian category. In this paper, we investigate the global $(\mathcal{X} , \mathcal{Y})$-Gorenstein projective dimension $\mathrm{gl.GPD}(\mathcal{X} ,\mathcal{Y})(\mathcal{A})$, associated to a GP-admissible pair $(\mathcal{X} , \mathcal{Y} )$. We give homological conditions over $(\mathcal{X} , \mathcal{Y})$ that characterize it. Moreover, given a GI-admisible pair $(\mathcal{Z} , \mathcal{W} )$, we study conditions under which $\mathrm{gl.GID}(\mathcal{Z},\mathcal{W})(\mathcal{A})$ and $\mathrm{gl.GPD}(\mathcal{X},\mathcal{Y})(\mathcal{A})$ are the same.
