K -Groups of Trivial Extensions and Gluings of Abelian Categories

Qinghua Chen and Min Zheng
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Qinghua Chen: School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117, China
Min Zheng: School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117, China

Mathematics, 2021, vol. 9, issue 16, 1-11

Abstract: This paper focuses on the K i -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, K i -groups of a certian subcategory of the trivial extension category is isomorphic to K i -groups of the similar subcategory of the original category. Moreover, under some conditions, we show that the K i -groups of a left (right) gluing of two abelian categories are isomorphic to the direct sum of K i -groups of two abelian categories. As their applications, we obtain some results of the K i -groups of the trivial extension of a ring by a bimodule ( i ? N ).

Keywords: abelian category; gluing of categories; K i -group; trivial extension of category; trivial extension ring (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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