Abstract
Let be a non-zero right module over a ring with identity. The weakly second submodules is studied in this paper. A non-zero submodule of is weakly second Submodule when , where , and is a submodule of implies either or . Some connections between these modules and other related modules are investigated and number of conclusions and characterizations are gained.
Highlights
Let be a non-zero right module over a ring with identity
In [4], we provide the idea of weakly secondary as a generalization of weakly second concept and in the same time it is a new type of secondary submodules and a dual notion of classical primary submodules respectively
We investigate the weakly second submodules idea and we supply examples (Remarks and Examples 2.3) and needful features of this concept
Summary
(4) Clearly every weakly second submodule is weakly secondary while the converse is not true by [3]. (6) The secondary submodules and weakly second concepts do not imply from each one to another. Module is weakly second but not secondary. (8) The following implication is clear coquasi-dedekind module divisible module second module weakly second module. (9) It is clear Z and Q as Z-modules are coquasi-dedekind ( and are divisible ) by (8). Z (where and prime numbers) and Q Q as Z-modules are divisible and weakly second. (10) If is weakly second module need not be coquasi-dedekind
Sign-in/Register to view highlights & summary 
Published Version (
Free)
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 call