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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Published in | Mathematics (Basel) Vol. 9; no. 16; p. 1864 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Basel
MDPI AG
01.08.2021
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Subjects | |
Online Access | Get full text |
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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). |
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ISSN: | 2227-7390 2227-7390 |
DOI: | 10.3390/math9161864 |