期刊
MATHEMATICS
卷 9, 期 16, 页码 -出版社
MDPI
DOI: 10.3390/math9161864
关键词
abelian category; gluing of categories; K-i-group; trivial extension of category; trivial extension ring
类别
资金
- National Natural Science Foundation of China [11871404, 11471269, 11601084]
This paper focuses on the Ki-groups of two types of extensions of abelian categories, the trivial extension and the gluing of abelian categories, showing isomorphisms of Ki-groups under certain conditions. The results provide a foundation for future research in related fields.
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 is an element of N).
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