Vol. 49, No. 2, 1973

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Radical properties involving one-sided ideals

R. F. Rossa

Vol. 49 (1973), No. 2, 467–471

A radical P is called strongly right hereditary (srh) if P(I) = I P(R) for every right ideal I of each (not necessarily associative) ring R in a suitable universal class W. This is a one-sided version of the concept of a strongly hereditary radical class investigated by W.G. Leavitt and R.L. Tangeman. A discussion parallel to theirs is obtained including a construction of the minimal srh radical class in W containing a given class. Srh radicals are related to a new radical construction obtained by modifying the lower radical construction of Tangeman and D. Kreiling.

Mathematical Subject Classification 2000
Primary: 16A21
Secondary: 17A99
Received: 28 September 1972
Revised: 12 December 1972
Published: 1 December 1973
R. F. Rossa