Vol. 55, No. 2, 1974

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A “going down” theorem for certain reflected radicals

Barry J. Gardner and Patrick Noble Stewart

Vol. 55 (1974), No. 2, 381–389

In a category 𝒦 suitable for radical theory, a functor Φ : 𝒦→𝒦 is studied which is associated with a natural transformation 1𝒦 Φ in a way which bears a formal resemblance to the behavior of certain “extension” functors of rings, such as that which assigns to each A the polynomial ring A[x]: every normal subobject N Φ(A) has a “contraction” Nc A. For a radical class in 𝒦 such that = {A|Φ(A) ∈ℛ} is also radical, some conditions are obtained which imply that (A) = (Φ(A))c.

Mathematical Subject Classification 2000
Primary: 18A99
Secondary: 16A21
Received: 4 December 1973
Published: 1 December 1974
Barry J. Gardner
Patrick Noble Stewart