Corrigendum

Abstract

The abstract of [1] should read as follows: We define nilpotent and strongly nilpotent elements of a module M and show that the set s M of all strongly nilpotent elements of a uniserial module M defined over a commutative unital ring coincides with the classical prime radical cl M the intersection of all classical prime submodules of M.Definition 2.1 of [1] should state as follows: an element m of an R-module M is strongly nilpotent if m = 0 or for every sequence a 1 a 2 a 3 with a 1 = a, a n+1 ∈ a n Ra n for all n and 0 = am = a t m for some positive integer t, there exists a positive integer k ≥ t such that a k m = 0.

Characterization of non-nilpotent elements of the Z-module Z/(p_1^{k_1} x...x p_n^{k_n})Z

“…In [5], it was generalized to strongly nilpotent elements. Strongly nilpotent elements of a uniserial module coincide with the classical prime radical of that module, see [5,Theorem 3.1] and [4]. This result generalizes that of Levitzki for rings, see [2,Theorem 2.6].…”