On exactness and splitting
TU, Shenzhen, China.
Review Article
World Journal of Advanced Research and Reviews, 2023, 20(02), 706–710
Article DOI: 10.30574/wjarr.2023.20.2.2344
Publication history:
Received on 06 October 2023; revised on 12 November 2023; accepted on 15 November 2023
Abstract:
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.
Keywords:
Exactness; Splitting; Modules; Ring; Short Exact Sequence
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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