局部同源性与Serre范畴

IF 4.9 1区数学 Q1 MATHEMATICS Acta Mathematica Pub Date : 2019-12-17 DOI:10.4467/20843828am.19.001.12109

Zahra Barqsouz, S. O. Faramarzi

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引用次数: 0

摘要

当局部同调模在R-模范畴的Serre子范畴中时，我们给出了一些结果。对于R的理想a，我们还定义了Serre范畴上条件C的概念，它似乎是Melkersson[1]中条件Ca的对偶。作为一个主要结果，我们证明了对于一个Artinian R-模M和R-模范畴的任何Serre子范畴S以及一个非负整数S，HomR（R/a，H，As（M））∈S如果Hi（M）∈S对于所有i>S。

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Local homology and Serre categories

We show some results about local homology modules when they are in a Serre subcategory of the category of R-modules. For an ideal a of R, we also define the concept of the condition C on a Serre category, which seems dual to the condition Ca in Melkersson [1]. As a main result we show that for an Artinian R-module M and any Serre subcategory S of the category of R-modules and a non-negative integer s, HomR(R/a,H a s(M)) ∈ S if Hi (M) ∈ S for all i > s.

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