Volume 20 No 12 (2022)
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A Study of Ws- Exact Sequence
Ashwani Kumar Garg
In the context of group theory, a sequence The sequence is called exact if it is exact at each {\displaystyle G_{i}}for all {\displaystyle 1\leqi<n}, i.e., if the image of each homomorphism is equal to the kernel of the next. The sequence of groups and homomorphisms may be either finite or infinite.A similar definition can be made for other algebraic structures. For example, one could have an exact sequence of vector spaces and linear maps, or of modules and module homomorphisms.More generally, the notion of an exact sequence makes sense inany category with kernels and cokernels, and more specially in abelian categories, where it is widely used
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