Abstract
Ris a ring with unity, and all modules are unitary right R-modules. The concept of compressiblemodules was introduced in 1981 by Zelmanowitz, where moduleMis called compressible if it can be embedded inany nonzero submoduleAofM. In other words, M is a compressible module if for each nonzero submoduleAofM, f∈Hom(M,A)exists, such thatfis monomorphism. Retractable modules were introduced in 1979 Khuri, wheremoduleMis retractable if Hom(M, A )6=0 for every nonzero submoduleAofM. We define a new notion, namely,essentially retractable module relative to a submodule. In addition, new generalizations of compressible modulesrelative to a submodule are introduced, where moduleMis called compressible module relative to a submoduleNofM. If for all nonzero submoduleKofMcontainsN, then a monomorphism f∈Hom(M, K) exists. Somebasic properties are studied and many relationships between these classes and other related concepts are presentedand studied. We also introduce another generalization of retractable module, which is called small kernel retractablemodule
Recommended Citation
Al-Aeashi, Shukur Neamah and Al-Bakaa, Fatimah Hussein
(2021)
"Essentially Retractable Modules Relative To A Submodule And Some Generalizations,"
Iraqi Journal for Computer Science and Mathematics: Vol. 2:
Iss.
2, Article 1.
DOI: https://doi.org/10.52866/ijcsm.2021.02.02.001
Available at:
https://ijcsm.researchcommons.org/ijcsm/vol2/iss2/1
