Corrigendum

This article refers to:

Generalization of Nilpotency of Ring Elements to Module Elements

Article title: “Generalization of Nilpotency of Ring Elements to Module Elements”

Authors: David Ssevviiri and Nico J. Groenewald

Journal: Communications in Algebra

Bibliornetrics: Volume 42, Issue 2, pages 571–577

DOI: 10.1080/00927872.2012.718822

The abstract of [1] should read as follows: We define nilpotent and strongly nilpotent elements of a module M and show that the set 𝒩 _s (M) of all strongly nilpotent elements of a uniserial module M defined over a commutative unital ring coincides with the classical prime radical β _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.

Propositions 2.3 and 2.4 of [1] are valid, when the above definition of a strongly nilpotent element of a module is appropriately used in the given proofs. Furthermore, Theorem 3.1 and Corollaries 3.1 and 3.2 of [1] are valid if on top of the given conditions the module is uniserial. A module is uniserial if its submodules are totally ordered by inclusion.

ACKNOWLEDGEMENT

We wish to thank Professor M. Behboodi for informing us of the errors in our paper [1].