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Note on the Singular Submodule
Published online by Cambridge University Press: 20 November 2018
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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.
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- Research Article
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- 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
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
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