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Baer cotorsion Pairs

Authors:	Lutz Strüngmann

Institution:	(1) Department of Mathematics, University of Duisburg-Essen, 45117 Essen, Germany

Abstract:	LetR be a unital associative ring and $\mathfrak{V},\mathfrak{W}$ two classes of leftR-modules. In St3] the notion of a ( $\mathfrak{V},\mathfrak{W}$ ) pair was introduced. In analogy to classical cotorsion pairs, a pair (V,W) of subclasses $\mathcal{V} \subseteq \mathfrak{V} and \mathcal{W} \subseteq \mathfrak{W}$ is called a ( $\mathfrak{V},\mathfrak{W}$ ) pair if it is maximal with respect to the classes $\mathfrak{V},\mathfrak{W}$ and the condition Ext _R ¹ (V, W)=0 for all $V \in \mathcal{V} and W \in \mathcal{W}$ . In this paper we study $\mathfrak{T}\mathfrak{f},\mathfrak{T}$ pairs whereR = ℤ and $\mathfrak{T}\mathfrak{f}$ is the class of all torsion-free abelian groups andT is the class of all torsion abelian groups. A complete characterization is obtained assumingV=L. For example, it is shown that every $\mathfrak{T}\mathfrak{f},\mathfrak{T}$ pair is singly cognerated underV=L. The author was supported by a DFG grant.

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