Geodesic
Note on the Singular Submodule
Canadian mathematical bulletin, Tome 13 (1970) no. 4, pp. 441-442

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

One very interesting and important problem in ring theory is the determination of the position of the singular ideal of a ring with respect to the various radicals (Jacobson, prime, Wedderburn, etc.) of the ring. A summary of the known results can be found in Faith [3, p. 47 ff.] and Lambek [5, p. 102 ff.]. Here we use a new technique to obtain extensions of these results as well as some new ones.Throughout we adopt the Bourbaki [2] conventions for rings and modules: all rings have 1, all modules are unital, and all ring homomorphisms preserve the 1. 
Fieldhouse, D. Note on the Singular Submodule. Canadian mathematical bulletin, Tome 13 (1970) no. 4, pp. 441-442. doi: 10.4153/CMB-1970-081-x
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[1] 1. Bass, H., Finitistic homological dimension and a homological generalization of semiprimary rings, Trans. Amer. Math. Soc. 95 (1960), 466-488. Google Scholar

[2] 2. Bourbaki, N., Algèbre Commutative, Ch. 1 and 2, Hermann, Paris, 1961. Google Scholar

[3] 3. Faith, C., Lectures on injective modules and quotient rings, Springer-Verlag, New York, 1967. Google Scholar

[4] 4. Johnson, R. E., The extended centralizer of a ring over a module, Proc. Amer. Math. Soc. 2 (1951), 891-895. Google Scholar

[5] 5. Lambek, J., Lectures on rings and modules, Blaisdell, Waltham, Mass., 1966. Google Scholar

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