Goldie Extending Modules

Corrigendum to: Goldie Extending Modules

“…By Corollary 2.5(i), S is right selfejective but not right self-injective even though M is injective as an R-module in this split-null extension." Lines 4-6 of the proof of the converse of Theorem 2.7 on p. 670 of Akalan et al [1] are in error. To correct this error, replace "H ∩ L .…”

Ojective ideals in modular lattices

“…Akalan, Birkenmeier and Tercan [1] and Lam [11] studied extending modules and the Goldie dimension of a module. Birkenmeier, Müller and Rizvi [2] used this concept to develop the theory of fully invariant extending modules.…”

A Characterization of Goldie Extending Modules Over Dedekind Domains

“…Recall that a module M is called extending (or CS ) if every submodule of M is essential in a direct summand of M (see, [5,10]). Recently, in [1] the authors have defined a module M to be G-extending (Goldie extending) if for each submodule X of M there is a direct summand D of M such that X ∩ D is essential in both X and D. Clearly every extending module is G-extending.…”

“…In [1] the decomposition theory of G-extending modules and essential extensions were investigated. Furthermore, it was shown that every canonical cogenerator is G-extending [1,Theorem 4.6]; but it is not, in general, extending.…”