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

Voir la notice de l'article provenant de la source Cambridge University Press

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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[1] 1. Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. 1, Math. Surveys no. 7, Amer. Math. Soc., Providence, R. I., 1961. Google Scholar

[2] 2. Connell, I. G., On the group ring, Canad. J. Math. 15 (1963), 650-685. Google Scholar

[3] 3. Luedeman, John K., A generalization of the concept of a ring of quotients, Canad. Math. Bull, (to appear). Google Scholar

[4] 4. Sanderson, D. F., A generalization of divisibility and injectivity in modules, Canad. Math Bull. 8 (1965), 505-513. Google Scholar

[5] 5. Utumi, Y., On continuous rings andself-injective rings, Trans. Amer. Math. Soc. 118 (1965), 158-173. Google Scholar

[6] 6. Wenger, R., Self-injective semigroup rings for finite inverse semigroups, Proc. Amer. Math. Soc. 20(1969), 213-216. Google Scholar

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