Geodesic
A Note on the Σ(S)-Injectivity of R(S)
Canadian mathematical bulletin, Tome 13 (1970) no. 4, pp. 481-489

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Let R be a ring with 1. All modules considered are to be unital left R-modules unless otherwise noted.Definition. A σ-set for R is a nonempty set Σ of left ideals of R satisfying the following conditions: (σ1) If I ∊ Σ, J is a left ideal of I, and J ⊇ I, then J ∊ Σ. (σ2) If I ∊ Σ and r ∊ R, then Ir-1 = {s ∊ R | sr ∊ I} ∊ Σ. (σ3) If I is a left ideal of R, J ∊ Σ, and It-1 ∊ Σ for each t ∊ J, then I ∊ Σ. 
Luedeman, John K. A Note on the Σ(S)-Injectivity of R(S). Canadian mathematical bulletin, Tome 13 (1970) no. 4, pp. 481-489. doi: 10.4153/CMB-1970-088-0
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     title = {A {Note} on the {\ensuremath{\Sigma}(S)-Injectivity} of {R(S)}},
     journal = {Canadian mathematical bulletin},
     pages = {481--489},
     year = {1970},
     volume = {13},
     number = {4},
     doi = {10.4153/CMB-1970-088-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-088-0/}
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