Radical and semisimple classes with specified properties

Leavitt, W. G.

doi:10.1090/S0002-9939-1970-0252454-2

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