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STRONGLY COTORSION (TORSION-FREE) MODULES AND COTORSION PAIRS

  • Yan, Hangyu
  • Received : 2009.04.10
  • Accepted : 2009.08.13
  • Published : 2010.09.30

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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