论文标题
子类别何时无用或扭转？
When is a subcategory Serre or torsionfree?
论文作者
论文摘要
让r成为一个可交换的noetherian戒指。用mod r表示有限生成的R模块的类别。在本文中，我们首先为MOD R的完整子类别提供了各种足够（和必要的）条件，使其成为Serre子类别，其中包括Stanley和Wang和Wang和Takahashi定理的几个改进，并提供了更简单的证明。接下来，我们考虑mod r的ike锁定子类别是无扭转的类。我们研究了某些模块，可以通过直接进行汇总和扩展来构建所有有限长度的模块，然后我们将其应用以表明Mod R的IKE闭合子类别是无托托free类的情况，而R r是一定的数值半群环。
Let R be a commutative noetherian ring. Denote by mod R the category of finitely generated R-modules. In the present paper, we first provide various sufficient (and necessary) conditions for a full subcategory of mod R 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 mod R 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 mod R are torsionfree classes in the case where R is a certain numerical semigroup ring.
