STRONGLY COTORSION (TORSION-FREE) MODULES AND COTORSION PAIRS

Title & Authors
STRONGLY COTORSION (TORSION-FREE) MODULES AND COTORSION PAIRS
Yan, Hangyu;

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 $\small{\mathcal{SC}_n}$-preenvelope and an ST $\small{\mathcal{F}_n}$-cover for any $\small{n\;{\in}\;\mathbb{N}}$ 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;
Language
English
Cited by
1.
Totally acyclic complexes, Journal of Algebra, 2017, 470, 300
2.
Gorenstein injective envelopes and covers over two sided noetherian rings, Communications in Algebra, 2017, 45, 5, 2238
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