K-Groups of Trivial Extensions and Gluings of Abelian Categories

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 sim...

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Bibliographic Details
Published inMathematics (Basel) Vol. 9; no. 16; p. 1864
Main Authors Chen, Qinghua, Zheng, Min
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2021
Subjects
abelian category
Categories
Gluing
gluing of categories
Ki-group
trivial extension of category
trivial extension ring
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Summary: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).
ISSN:2227-7390
2227-7390
DOI:10.3390/math9161864