Geodesic
Free and Injective Lie Modules*
Canadian mathematical bulletin, Tome 9 (1966) no. 1, pp. 29-42

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We study free and injective Lie modules by investigating the relationship between Lie modules and (associative) modules. An important role is played by the universal enveloping ring of a Lie ring [4]. If L is an arbitrary Lie ring and W(L) its universal enveloping ring, we show that the category of Lie L-modules and the category of associative W(L)-module s are isomorphic (section 2). In section 3 we study free Lie modules and show how they may be obtained from free associative modules. A Lie module is free if and only if it is a direct sum of copies of the free Lie module on one generator. 
Kleiner, Israel. Free and Injective Lie Modules*. Canadian mathematical bulletin, Tome 9 (1966) no. 1, pp. 29-42. doi: 10.4153/CMB-1966-004-5
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     author = {Kleiner, Israel},
     title = {Free and {Injective} {Lie} {Modules*}},
     journal = {Canadian mathematical bulletin},
     pages = {29--42},
     year = {1966},
     volume = {9},
     number = {1},
     doi = {10.4153/CMB-1966-004-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-004-5/}
}
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