Abstract
In the category of left modules over a unital ring we show that a left exact reflector determines, for each n ⩾ 1 , a torsion theoretic setting in which universal extensions of length n exist. Combined with recent work of Rodelo and van der Linden (2011) [9] this establishes the existence of universal central extensions of groups and Lie algebras. Interpreted in the homotopy category of topological spaces, it provides a new perspective on existing results about Quillenʼs plus construction and its effect on homotopy groups.
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