Open AccessW-visible submodules and W-fully visible modules
Author(s) -
Mahmood S. Fiadh,
Buthy. Shihab,
Munther H. Abed
Publication year - 2020
Publication title -
iraqi journal for computer science and mathematics
Language(s) - English
Resource type - Journals
eISSN - 2958-0544
pISSN - 2788-7421
DOI - 10.52866/ijcsm.2019.01.01.005
Subject(s) - visible spectrum , ideal (ethics) , ring (chemistry) , mathematics , pure mathematics , physics , optoelectronics , chemistry , philosophy , organic chemistry , epistemology
In this paper, we presented a special type of submodule named W-visible submodule, which is weakerthan the visible submodule, where a proper submodule W of a T-module X is said to be W-visible if W = IW for somenon-zero proper ideal I of T. Also, we presented the concept of W-fully visible module, where a module X over aring T is said to be W-fully visible if any proper submodule of X is W-visible submodule. This concept is consideredweaker than the concept of fully visible module. In this study, we achieved numerous results and characteristics thatbelong to this concept