Radical and semisimple classes with specified properties
HTML articles powered by AMS MathViewer
- by W. G. Leavitt PDF
- Proc. Amer. Math. Soc. 24 (1970), 680-687 Request permission
Erratum: Proc. Amer. Math. Soc. 25 (1970), 922.
Abstract:
Conditions are given on a radical (semisimple) property to ensure the existence of a construction for the smallest radical (semisimple) class with the property, containing a given class of rings. This generalizes earlier results on smallest hereditary or strongly hereditary radical classes, and hereditary semisimple classes. In the last section certain classes of rings are shown to admit a construction for the largest radical (semisimple) class contained in the given class. This leads to theorems on largest radical (semisimple) classes dual to the already established smallest theorems.References
- W. G. Leavitt, Strongly hereditary radicals, Proc. Amer. Math. Soc. 21 (1969), 703–705. MR 240152, DOI 10.1090/S0002-9939-1969-0240152-2
- W. G. Leavitt, Hereditary semisimple classes, Glasgow Math. J. 11 (1970), 7–8. MR 258897, DOI 10.1017/S0017089500000781
- Ju. M. Rjabuhin, On imbeddings of radicals, Bul. Akad. Štiince RSS Moldoven. 1963 (1963), no. 11, 34–41 (1964) (Russian, with Moldavian summary). MR 207757
- Nathan Divinsky, Rings and radicals, Mathematical Expositions, No. 14, University of Toronto Press, Toronto, Ont., 1965. MR 0197489
- W. G. Leavitt and E. P. Armendariz, Nonhereditary semisimple classes, Proc. Amer. Math. Soc. 18 (1967), 1114–1117. MR 220786, DOI 10.1090/S0002-9939-1967-0220786-X
- A. E. Hoffman and W. G. Leavitt, Properties inherited by the lower radical, Portugal. Math. 27 (1968), 63–66. MR 262278
- Ju. M. Rjabuhin, Lower radicals of rings, Mat. Zametki 2 (1967), 239–244 (Russian). MR 217129
Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 24 (1970), 680-687
- MSC: Primary 17.10
- DOI: https://doi.org/10.1090/S0002-9939-1970-0252454-2
- MathSciNet review: 0252454