论文标题
深度，熟练级别和有限维度
The depth, the delooping level and the finitistic dimension
论文作者
论文摘要
我们调查了Noetherian半融合环的两个不变式，即我们称为“ Delooping Level”的深度和新不变。这些分别给出了有限尺寸的上限和上限。首先，我们给出了一个必要和足够的标准，即在相关邻接的单位映射的分裂方面为delooping级别提供有限的标准，并使用它来提供足够的扭转标准以实现有限。我们进一步将这些不变性与模块的Auslander-Bridger等级条件联系起来，这些模块的条件正在消失在双分配双重上。作为主要定理，我们证明，每当对简单模块的第一个非平凡等级条件感到满足时，这些界限都同意，以便在这种情况下，要么不变性计算有限的维度。在Artinian戒指上，我们表明，Delooping级别也界定了巨大的有限维度，并且我们获得了足够的共同体学标准，即首个有限的维度猜想。这些条件始终保持在换向的局部赛车上，我们将深度作为环的深度级别获得了新的特征。
We investigate two invariants of Noetherian semiperfect rings, namely the depth and a new invariant we call the "delooping level". These give lower and upper bounds for the finitistic dimension, respectively. As first theorems, we give a necessary and sufficient criterion for the delooping level to be finite in terms of the splitting of the unit map of a related adjunction, and use this to give a sufficient torsionfreeness criterion for finiteness. We further relate these invariants to the Auslander-Bridger grade conditions for modules, which are vanishing conditions on double Ext duals. As main theorem, we prove that these bounds agree whenever the first non-trivial grade conditions are satified for simple modules, so that either invariant computes the finitistic dimension in this case. Over Artinian rings, we show that the delooping level also bounds the big finitistic dimension, and we obtain a sufficient cohomological criterion for the first finitistic dimension conjecture to hold. Over commutative local Noetherian rings, these conditions always hold and we obtain a new characterisation of the depth as the delooping level of the ring.
