Semi-Essentially Compressible Modules and Semi-Essentially Retractable Modules - Al Hakeem, Mohammed Baqer Hashim; Al-Mothafar, Nuhad Salim (Iraqi Journal of Science, 2023)
Let  be a commutative ring with 1 and  be a left unitary . In this paper, the generalizations for the notions of compressible module and  retractable module are given.An   is termed to be  semi-essentially compressible if   can be embedded in every of a non-zero semi-essential submodules. An  is termed a semi-essentially retractable module, if   for every non-zero semi-essentially submodule of an . Some of their advantages characterizations and examples are given.  We also study the relation between these classes and some other classes of modules.