Abstract
We introduce Rad-discrete and quasi-Rad-discrete modules as a proper generalization of (quasi) discrete modules, and provide various properties of these modules. We prove that a direct summand of a (quasi) Rad-discrete module is (quasi) Rad-discrete. We show that every projective R-module is (quasi) Rad-discrete if and only if R is left perfect. We also prove that, over a commutative Noetherian ring R, every quasi-Rad-discrete R-module is the direct sum of local R-modules if and only if R is Artinian. Finally, we investigate self-projective Rad-discrete modules and $$\pi $$ -projective quasi-Rad-discrete modules over Dedekind domains.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
