Bulletin of the
Korean Mathematical Society BKMS

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