journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-2031 On semi-continuous and quasi-semi-continuous modules  Abdulrazzaq Zaid Abdulaziz Department of Mathematics and Computer Applications, College of Science, Al-Muthanna University, Samawah, Iraq Nayef Mahdi Saleh Department of Mathematics, College of Education, Mustensiriyah University, Baghdad, Iraq Hbaib Mohamed Department of Mathematics, College of Science, Safx University, Safx, Tunisia 28 4-A 1051 1058 26 06 2025

 In our research paper, we will introduce some classes of modules named (semi-continuous modules and quasi-semi-continuous modules) (briefly, SECO-modules and Q-SECO-modules), which are proper generalizations of both continuous and quasi-continuous modules, respectively. Also, we studied numerous properties of those concepts and discussed the connections between semi-extending and semi-continuous modules and some of the ideas of well-known modules. Some known results on (quasi-)continuous modules are generalized to our concepts. In addition, we have discussed the hereditary property of (SECS-module, SECO-module, and Q-SECO-module).

 Extending modules Semi-extending modules Continuous modules SECO modules Q-SECO modules access open retracted no