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General hereditary for radical theory

Published online by Cambridge University Press:  20 January 2009

R. F. Rossa  and
R. L. Tangeman
R. L. Tangeman
Affiliation:
Arkansas State University, Arkansas 72467
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Let W be a class of not necessarily associative rings which is universal in the sense that it is closed under homomorphic images and is hereditary to subrings. All rings considered will be assumed to belong to W. The notation I ⊲ R will mean I is an ideal of R. A relation σ on W will be called an H-relation if σ satisfies the properties:

(1) I σ R implies I is a subring of R.

(2) If I σ R and ø is a homomorphism of R, then IØ σ Rø.

(3) If I σ R and J is an ideal of R, then I ∩ J σ J.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 20 , Issue 4 , September 1977 , pp. 333 - 337
Copyright
Copyright © Edinburgh Mathematical Society 1977

References

REFERENCES

(1) Divinsky, N. J., Rings and radicals (George Allen and Unwin, London, 1965).Google Scholar
(2) Enersen, P. O. and Leavitt, W. G., The upper radical construction, Publ. Math. Debrecen 20 (1973), 219–222.CrossRefGoogle Scholar
(3) Hoffman, A. E. and Leavitt, W. G., Properties inherited by the lower radical, Port. Math. 27 (1968), 63–66.Google Scholar
(4) Kreiling, D. and Tangeman, R., Lower radicals in non-associative rings, J. Australian Math. Soc. 14 (1972), 419–23.Google Scholar
(5) Leavitt, W. G., Lower Radical Constructions, Coll. Math. Sac. Janos Bolyai 6. Rings, Modules and Radicals. (Kesathely (Hungary), 1971).Google Scholar
(6) Leavitt, W. G., Strongly hereditary radicals, Proc. Amer. Math. Soc. 21 (1969), 703–705.CrossRefGoogle Scholar
(7) Rossa, R. F., More properties inherited by the lower radical, Proc. Amer. Math. Soc. 33 (1972), 247–249.Google Scholar
(8) Rossa, R. F., Radical properties involving one-sided ideals, Pacific J. Math. 49 (1973), 467–471.CrossRefGoogle Scholar
(9) Tangeman, R. L., Strong heredity in radical classes, Pacific J. Math. 42 (1972), 259–265.CrossRefGoogle Scholar