Bulletin of the
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Bull. Korean Math. Soc. 2010; 47(5): 1041-1052

Published online September 1, 2010 https://doi.org/10.4134/BKMS.2010.47.5.1041

Copyright © The Korean Mathematical Society.

Strongly cotorsion (torsion-free) modules and cotorsion pairs

Hangyu Yan

Nanjing University

Abstract

In this paper, strongly cotorsion (torsion-free) modules are studied and strongly cotorsion (torsion-free) dimension is introduced. It is shown that every module has a special $\mathcal{S}\mathcal{C}_n$-preenvelope and an $\mathcal{S}\mathcal{T}\mathcal{F}_n$-cover for any $n\in\mathbb{N}$ based on some results of cotorsion pairs from [9]. Some characterizations of strongly cotorsion (torsion-free) dimension of a module are given.

Keywords: strongly cotorsion module, strongly torsion-free module, cotorsion pair, strongly cotorsion dimension, strongly torsion-free dimension

MSC numbers: 16E30, 16E10

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