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A simple ring separating certain radicals

Published online by Cambridge University Press:  18 May 2009

G. A. P. Heyman  and
W. G. Leavitt
G. A. P. Heyman
Affiliation:
University of the Orange Free State, Bloemfontein, South Africa
W. G. Leavitt
Affiliation:
University of Nebraska-Lincoln, U. S. A.
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All rings considered will be associative. For a class M of rings let UM be the class of all rings having no non-zero homomorphic image in M. A hereditary class M of prime rings is called a “special class” [see 1, p. 191] if it has the property that when I ∈ M with I an ideal of a ring R, then R/I* ∈ Mwhere I* is the annihilator of I in R, and the corresponding radical class UM is then a “special radical”. Let S be the class of all subdirectly irreducible rings with simple heart.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 16 , Issue 1 , March 1975 , pp. 29 - 31
Copyright
Copyright © Glasgow Mathematical Journal Trust 1975

References

REFERENCES

1.Andrunakievitch, V. A., Radicals of Associative rings I, Mat. Sbornik 44 (1958), 179–212.Google Scholar
2.Behrens, A. E., Nichtassoziative Ringe, Math. Ann. 127 (1954), 441–452.CrossRefGoogle Scholar
3.Jacobson, Nathan, Structure of Rings, Amer. Math. Soc. Colloq. Publ. vol. 37, 1964.Google Scholar
4.Leavitt, W. G., The module type of a ring, Trans'. Amer. Math. Soc. 103 (1962), 113–120.CrossRefGoogle Scholar
5.Leavitt, W. G., The module type of homomorphic images, Duke Math. J. 32 (1965), 305–311.CrossRefGoogle Scholar