K-groups of trivial extensions and gluings of abelian categories
K-groups of trivial extensions and gluings of abelian categories
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阿贝尔范畴的平凡扩展和粘合的 K 群
DOI：
10.3390/math9161864
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发表时间：
2021
期刊：
影响因子：
2.4
通讯作者：
Min Zheng
中科院分区：
文献类型：
--
作者：
Qinghua Chen;Min Zheng
本文研究了两类阿贝尔范畴的扩展的ki群，即阿贝尔范畴的平凡扩展和粘接。证明了在一定条件下，平凡扩展范畴的某子范畴的ki群与的ki群是同构的。原类别的类似子类别。此外，在一定条件下，我们证明了两个阿贝尔范畴的左（右）胶合的ki群与两个阿贝尔范畴的ki群的直和是同构的。作为它们的应用，我们得到了的ki群的一些结果。双模（i∈N）对环的平凡扩展…
This paper focuses on the Ki-groups of two types of extensions of abelian categories, which are the trivial extension and the gluing of abelian categories. We prove that, under some conditions, Ki-groups of a certian subcategory of the trivial extension category is isomorphic to Ki-groups of.the similar subcategory of the original category. Moreover, under some conditions, we show that the Ki-groups of a left (right) gluing of two abelian categories are isomorphic to the direct sum of Ki-groups of two abelian categories. As their applications, we obtain some results of the Ki-groups of.the trivial extension of a ring by a bimodule (i ∈ N)..