Abstract
Motivated by [2] and [6], we introduce a generalization of extending (CS) modules by using the concept of τ-large submodule which was defined in [9]. We give some properties of this class of modules and study their relationship with the familiar concepts of τ-closed, τ-complement submodules and the other generalization of extending modules (τ-complemented, τ-CS, s−τ-CS modules). We are also interested in determining when a τ-divisible module is τ-extending. For a τ-extending module M with C3, we obtain a decomposition theorem that there is a submodule K of M such that \(M = \tau (M)\,\oplus\,K\) and K is τ (M)-injective. We also treat when a direct sum of τ-extending modules is τ-extending.
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Çeken, S., Alkan, M. On τ-Extending Modules. Mediterr. J. Math. 9, 129–142 (2012). https://doi.org/10.1007/s00009-010-0096-2
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DOI: https://doi.org/10.1007/s00009-010-0096-2