Where does the notation $\mbox{Soc}(M)$ (the sum of all simple submodules of a module $M$) first appear?
This book by J. Lambek says on page 168 that the notion of socle (for modules) is due to Dieudonne. In this paper, the word "socle" is used by Dieudonne, and he explains that he follows M.R. Remak, who first introduced the notion of socle for finite groups, as a subgroup generated by all minimal normal subgroups. However, I cannot find yet where the notation "Soc" appears first (in the context of modules). Hope this bit of information helps. Cheers! 


Just to establish some more reference points: In the book In the paper In the book 

