TU, Shenzhen, China.
World Journal of Advanced Research and Reviews, 2023, 20(02), 706–710
Article DOI: 10.30574/wjarr.2023.20.2.2344
DOI url: https://doi.org/10.30574/wjarr.2023.20.2.2344
Received on 06 October 2023; revised on 12 November 2023; accepted on 15 November 2023
In this paper, we study the concepts of exactness and splitting in exact sequences of modules over a ring. We review some basic definitions and properties of exact sequences, and introduce the notions of short exact sequences, split exact sequences, projective modules, injective modules, and semisimple modules. We prove some important results relating these concepts, such as the splitting lemma. We also give some examples and applications of these results.
Exactness; Splitting; Modules; Ring; Short Exact Sequence
Get Your e Certificate of Publication using below link
Preview Article PDF
YANG LIU. On exactness and splitting. World Journal of Advanced Research and Reviews, 2023, 20(02), 706–710. Article DOI: https://doi.org/10.30574/wjarr.2023.20.2.2344
Copyright © 2023 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution Liscense 4.0