标题： 戈沃罗夫-拉扎德和Gorenstein及限制同调维数的有限可构造性 显示英文标题

标题： Govorov--Lazard and finite deconstructibility for Gorenstein and restricted homological dimensions

摘要： 在允许点对偶化模的 Cohen--Macaulay 环上，我们证明了受限制的投射维数被任何整数所限制的模类是有限可构造的，并且受限制的平坦维数被任何整数所限制的模类满足 Govorov-Lazard 性质。 在这一过程中，我们证明了在（局部）Gorenstein 环上关于 Gorenstein 投射和平坦维数的相应结果。 在 Cohen--Macaulay 环之外，我们考虑了受限制的投射维数为零和受限制的平坦维数为零的类似性质，并在有限 Krull 维数的交换 Noether 环上建立了这些性质。 这在某些情况下导致了有限生成模类的预包络性质，并提供了 Holm 关于平衡大 Cohen--Macaulay 模结构结果在不同方向上的推广。 显示英文摘要

摘要： Over Cohen--Macaulay rings admitting a pointwise dualizing module, we show that the class of modules of restricted projective dimension bounded by any integer is finitely deconstructible and that the class of modules of restricted flat dimension bounded by any integer satisfies the Govorov-Lazard property. Along the way, we prove the corresponding result for Gorenstein projective and flat dimensions over (locally) Gorenstein rings. Outside of Cohen--Macaulay rings, we consider analogous properties for restricted projective dimension zero and restricted flat dimension zero and establish them for commutative noetherian rings of finite Krull dimension. This has consequences for the corresponding classes of finitely generated modules being preenveloping in certain cases and provides generalizations of Holm's results on structure of balanced big Cohen--Macaulay modules in various directions.