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K -Groups of Trivial Extensions and Gluings of Abelian Categories

Author

Listed:
  • 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
    Department of Mathematics and Physics, Fujian Jiangxia University, Fuzhou 350108, China)

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 ).

Suggested Citation

  • Qinghua Chen & Min Zheng, 2021. "K -Groups of Trivial Extensions and Gluings of Abelian Categories," Mathematics, MDPI, vol. 9(16), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1864-:d:609414
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