Weak ideal invariance and orders in artinian rings: Corrigendum

Abstract

Let R be an associative ring with identity element which has Krull dimension on the left (see [3] for the relevant definitions). For any ordinal α, and any module RX, let τα(X) denote the sum in. X of all cyclic submodules of Krull dimension less than α. (The Krull dimension of a module X will be denoted by |x|.) It is clear that if X' is a submodule of X, then τα(X) = X' ∩ τα(X) and that f[τα(X)] ⊆ τα(Y) for any R-homomorphism f: X→Y. Thus τα defines a torsion preradical.