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http://dx.doi.org/10.4134/BKMS.2010.47.5.1041

STRONGLY COTORSION (TORSION-FREE) MODULES AND COTORSION PAIRS  

Yan, Hangyu (DEPARTMENT OF MATHEMATICS NANJING UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.5, 2010 , pp. 1041-1052 More about this Journal
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 $\mathcal{SC}_n$-preenvelope and an ST $\mathcal{F}_n$-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;
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