Further Notes on Tightness
Rings and Algebras
2025-12-09 v3
Abstract
Tight and essentially tight modules generalize weakly injective modules. Essential tightness requires embeddings to be essential. This restriction makes the two notions totally different. In this note, we investigate cases when those two notions are the same. Moreover, we look at the cases when essentiallity is imposed only on one of the embeddings rather than both. This allows defining a special class of tight and essentially tight modules and a generalization of both.
Keywords
Cite
@article{arxiv.2411.12410,
title = {Further Notes on Tightness},
author = {Nasief Khlaif and Mohammad Saleh},
journal= {arXiv preprint arXiv:2411.12410},
year = {2025}
}
Comments
Rewritten parts of the paper making sure it well-written