标题： 某些 Cohen-Macaulay 模的性质以及通过 (同调) 上同调有限消失来判断局部环的条件 显示英文标题

标题： Test properties of some Cohen-Macaulay modules and criteria for local rings via finite vanishing of (co)homologies

摘要： 在本文中，我们推导了CM（Cohen-Macaulay）模的测试性质，在有限多个Ext或Tor消失的意义下，这些CM模的乘数和生成元数量（或类型）由某些不等式相关联。 我们将这些测试行为与其他结果结合，通过涉及此类CM模的Ext或Tor的有限消失来表征各种局部环，包括乘数最多为二的超曲面环。 作为进一步的应用，我们验证了每个最小乘数的CM模的长期存在的（广义）Auslander-Reiten猜想。 显示英文摘要

摘要： In this article, we deduce test properties, in the sense of finitely many vanishing of Ext or Tor, of CM (Cohen-Macaulay) modules whose multiplicity and number of generators (resp., type) are related by certain inequalities. We apply these test behaviour, along with other results, to characterize various kinds of local rings, including hypersurface rings of multiplicity at most two, via finite vanishing of Ext or Tor involving such CM modules. As further applications, we verify the long-standing (Generalized) Auslander-Reiten Conjecture for every CM module of minimal multiplicity.