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If (R,M) and (S,N) are quasilocal (commutative integral) domains and f : R → S is a (unital) ring homomorphism, then f is said to be a strong local homomorphism (resp., radical local homomorphism) if f (M) = N (resp., f (M) ⊆ N and for each x ∈ N, there exists a positive integer t such that x t ∈ f (M)). It is known that if f : R → S is a strong local… (More)
A collection of results are presented which are loosely centered around the notion of reflective subcategory. For example, it is shown that reflective subcategories are orthogo-nality classes, that the morphisms orthogonal to a reflective subcategory are precisely the morphisms inverted under the reflector, and that each subcategory has a largest " envelope… (More)