Kernel-Cokernel Sequence for Composition and its Applications

Abstract

If this article, an elementary kernel-cokernel exact sequence is introduced for $A\stackrel{f}{\to }B\stackrel{g}{\to }C$. Some relative sequences and applications are dicussed. This result can simplify some proofs---the indices of Frodholm operators, Harada and Sai theorem, and the derived couples of exact couples.