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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

$G$-projective groups


Authors: C. Vinsonhaler and W. Wickless
Journal: Proc. Amer. Math. Soc. 92 (1984), 164-166
MSC: Primary 20K15; Secondary 20K40
DOI: https://doi.org/10.1090/S0002-9939-1984-0754694-2
MathSciNet review: 754694
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Abstract: Let TF be the category of torsion free abelian groups of finite rank and homomorphisms. For $G$ in TF let ${\text {PC}}\left ( G \right )$ be the projective class in TF generated by $\left \{ G \right \}$. Theorem. ${\text {PC}}\left ( G \right )$ consists exactly of groups of the form $P \oplus F$, where $F$ is finite rank free and $P$ is $G$-projective $P \oplus P’ \cong {G^n}$ for some positive integer $n$).


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Article copyright: © Copyright 1984 American Mathematical Society