Abstract
Baer’s Lemma [9, Proposition 86.5] proved to be a useful tool for discussing decompositions of torsion-free abelian groups. If for abelian groups A and G the A-socle SA(G) of G is the subgroup of G generated by all f(A) where f ∈ HomZ(A,G) and G is A-projective if it is isomorphic to a direct summand of ⊕I A, then Baer’s Lemma can be formulated in the following way without using types.
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Albrecht, U. (1983). Endomorphism Rings and A-Projective Torsion-free Abelian Groups. In: Göbel, R., Lady, L., Mader, A. (eds) Abelian Group Theory. Lecture Notes in Mathematics, vol 1006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21560-9_9
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DOI: https://doi.org/10.1007/978-3-662-21560-9_9
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