|
|||||
|
|
|
|
|
|
|
|
|
A
“going down” theorem for certain reflected radicals
Barry J. Gardner and Patrick Noble Stewart |
|
Vol. 55 (1974), No. 2, 381–389
|
Abstract |
|
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 ℛ in 𝒦 such that ℛ∗ = {A|Φ(A) ∈ℛ} is also radical, some conditions are obtained which imply that ℛ∗(A) = ℛ(Φ(A))c. |
Mathematical Subject Classification 2000
Primary: 18A99
Secondary: 16A21
|
Milestones
Received: 4 December 1973
Published: 1 December 1974
|
Authors |
| Barry J. Gardner | |
| Patrick Noble Stewart | |
|
