关于张量积的深度与自反性
On the depth and reflexivity of tensor products
AI总结：
本文研究交换Noether局部环上同调有限复形的张量积深度，给出超曲面环上有限生成模的非零张量积为自反模的新条件，并借助Asgharzadeh的结果在附录中探讨超曲面环上素理想张量积的自反性。
摘要：
本文研究交换Noether局部环上同调有限复形的张量积的深度。作为主要结果的一个应用，我们确定了若干新条件：在这些条件下，超曲面环上有限生成模的非零张量积仅当它的两个因子都自反时才可以是自反的。Asgharzadeh的一个结果表明，局部环中素理想的非零符号幂不可能具有有限投射维数，除非所讨论的环是整环。我们在附录中利用这一结论，研究了超曲面环上素理想的张量积的自反性。
英文摘要：
In this paper we study the depth of tensor products of homologically finite complexes over commutative Noetherian local rings. As an application of our main result, we determine new conditions under which nonzero tensor products of finitely generated modules over hypersurface rings can be reflexive only if both of their factors are reflexive. A result of Asgharzadeh shows that nonzero symbolic powers of prime ideals in a local ring cannot have finite projective dimension, unless the ring in question is a domain. We make use of this fact in the appendix and consider the reflexivity of tensor products of prime ideals over hypersurface rings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
