journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-2103 Radical small submodules and hollow modules Al-Mothafar Nuhad S. Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq Alzubiadey Zainab T. Department of Chemistry, College of Science, University of Baghdad, Baghdad, Iraq 28 4-A 1131 1136 26 06 2025

In this work, we give a new generalization for two important classes in the category of modules. There are Rad-small and Rad-hollow R-module. In this work, some properties and results of these submodule are given: A non-zero direct summand of any R-mod D is not Rad-small. Moreover, another characterization of Rad-hollow modules. 

 Small submodules Hollow modules Radical small submodules Maximal submodules access open retracted no