Vol. 42, No. 1, 1972

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Strong heredity in radical classes

Richard Tangeman

Vol. 42 (1972), No. 1, 259–265

In a recent paper, W. G. Leavitt has called a radical class 𝒫 in a universal class 𝒲 of not necessarily associative rings strongly hereditary if 𝒫(I) = I ∩𝒫(R) for all ideals I of any ring R ∈𝒲. In this paper, strongly hereditary radicals are investigated and a new construction is provided for the minimal strongly hereditary radical containing a given class in 𝒲. Nonassociative versions of some results of E. P. Armendariz on semisimple classes are proved, including a characterization of semisimple classes corresponding to strongly hereditary radicals.

Mathematical Subject Classification 2000
Primary: 17A99
Secondary: 08A25
Received: 12 April 1971
Published: 1 July 1972
Richard Tangeman