When is a subcategory Serre or torsionfree?
When is a subcategory Serre or torsionfree?
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发表时间：
2022-03
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通讯作者：
Kei-ichiro Iima;H. Matsui;Kaori Shimada;Ryo Takahashi
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作者：
Kei-ichiro Iima;H. Matsui;Kaori Shimada;Ryo Takahashi
设R是一个交换诺瑟环。用modR表示有限生成的r模的范畴。本文首先给出了modR的满子范畴是Serre子范畴的各种充分（必要）条件，其中包括Stanley和Wang定理以及Takahashi定理的若干改进，并给出了更简单的证明。接下来我们考虑什么时候modR的艾克闭子范畴是一个无扭类。我们研究了一些模，在这些模中，所有有限长度的模都可以通过直接求和和扩展得到，然后我们应用它证明了当R是一个数值半群环时，modR的艾克闭子范畴是无扭转类。
Let R be a commutative noetherian ring. Denote by modR the category of finitely generated R-modules. In the present paper, we first provide various sufficient (and necessary) conditions for a full subcategory of modR to be a Serre subcategory, which include several refinements of theorems of Stanley and Wang and of Takahashi with simpler proofs. Next we consider when an IKE-closed subcategory of modR is a torsionfree class. We investigate certain modules out of which all modules of finite length can be built by taking direct summands and extensions, and then we apply it to show that the IKE-closed subcategories of modR are torsionfree classes in the case where R is a certain numerical semigroup ring.