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Note on the Singular Submodule

Published online by Cambridge University Press:  20 November 2018

D. Fieldhouse
D. Fieldhouse*
Affiliation:
Queen's University, Kingston, Ontario
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 4 , December 1970 , pp. 441 - 442
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Bass, H., Finitistic homological dimension and a homological generalization of semiprimary rings, Trans. Amer. Math. Soc. 95 (1960), 466-488.Google Scholar
2. Bourbaki, N., Algèbre Commutative, Ch. 1 and 2, Hermann, Paris, 1961.Google Scholar
3. Faith, C., Lectures on injective modules and quotient rings, Springer-Verlag, New York, 1967.Google Scholar
4. Johnson, R. E., The extended centralizer of a ring over a module, Proc. Amer. Math. Soc. 2 (1951), 891-895.Google Scholar
5. Lambek, J., Lectures on rings and modules, Blaisdell, Waltham, Mass., 1966.Google Scholar