论文标题
在AB5*模块上具有Noetherian尺寸
On AB5* modules with Noetherian dimension
论文作者
论文摘要
在本文中，我们研究了某些模块总和的Noetherian维度。事实证明，对于任何模块M，如果M具有有限的跨度尺寸（FSD模块，简称为FSD），则每个模块的子模块总和均小于Alpha，或者它是一个弱原子模块，然后是Noetherian Dimension M比Alpha小。 Here, by a weakly atomic module we mean a module M for which every proper non-small submodule N, has Noetherian dimension strictly less than that of M. Also, it is proved that if M is an AB5* module with Noetherian dimension and N_i is a family of submodules of M such that Noetherian dimension M over N_i, less than alpha, for each i, then Noetherian dimension M over intersection of N_is less比alpha。使用此方法，我们为AB5*类别中的Alpha-Short模块提供了一个结构定理，最后，我们将Alpha-Short模块分类为此类别。
In this paper, we study the Noetherian dimension of sum of certain modules. It is proved that for any module M which is an irredundant sum of submodules, each of which has Noetherian dimension less than alpha, if M has finite spanning dimension (fsd-module, for short) or it is a weakly atomic module, then Noetherian dimension M less than alpha. Here, by a weakly atomic module we mean a module M for which every proper non-small submodule N, has Noetherian dimension strictly less than that of M. Also, it is proved that if M is an AB5* module with Noetherian dimension and N_i is a family of submodules of M such that Noetherian dimension M over N_i, less than alpha, for each i, then Noetherian dimension M over intersection of N_is less than alpha. Using this, we give a structure theorem for alpha-short modules in the category of AB5* and finally, we classify alpha-short modules in this category.
